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MATHEMATICS (647 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 21)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 5)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 6)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 5)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 3)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 9)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Biostatistics     Open Access   (Followers: 9)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 3)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 7)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 8)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 6)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 4)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 18)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 3)
BIBECHANA     Open Access  
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 7)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 17)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 2)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 2)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 1)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 9)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 4)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 12)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 3)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 3)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)
Foundations and Trends® in Econometrics     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Differential Equations and Dynamical Systems
  [SJR: 0.475]   [H-I: 9]   [2 followers]  Follow
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0974-6870 - ISSN (Online) 0971-3514
   Published by Springer-Verlag Homepage  [2345 journals]
  • Looking for an Efficient and Safe Hyperthermia Therapy: Insights from a
           Partial Differential Equations Based Model
    • Authors: Maria C. Quintero; Juan M. Cordovez
      Pages: 137 - 150
      Abstract: In the present study, we formulate a boundary value problem that characterizes the light and heat transfer processes in a tissue during a hypothetical superficial hyperthermia therapy. The heating process is represented with a partial differential equations system (PDEs) consisting in the diffusion and bio-heat equations whereas the tissue damage process is modeled with the Arrhenius integral equation. The PDEs system is discretized using the method of lines to obtain an ordinary differential equations system that approximates the original PDEs. The resulting model is then numerically solved to obtain (1) the spatio-temporal distribution of both absorbed light and heat, (2) the volume of tissue effectively treated, and (3) the degree of thermal damage reached. Finally, we define an optimization problem to find a set of relevant parameter values that maximize the therapeutic effect while minimizing damage to healthy tissue. The results of this work could be useful for preclinical level research, in particular for the study of strategies that modify the physical properties of the target tissue for a safe and efficient heat therapy.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0256-8
      Issue No: Vol. 25, No. 2 (2017)
  • Numerical Study on Binary Nanofluid Convection in a Rotating Porous Layer
    • Authors: Jyoti Sharma; Urvashi Gupta; R. K. Wanchoo
      Pages: 239 - 249
      Abstract: The present paper investigates the convection in a binary nanofluid layer in porous medium under the influence of rotation using Darcy–Brinkman model. A set of partial differential equations based on conservation laws for binary nanofluid convection are solved using Normal mode technique and one term weighted residual method. The problem is analyzed for both stationary as well as oscillatory convection for free-free boundaries of the layer. The oscillatory motions come into existence for bottom heavy configuration of nanoparticles in the fluid layer. As far as thermal Rayleigh number is concerned, it does not show much variation with respect to different nanoparticles (alumina, copper, titanium oxide, silver) for bottom heavy configuration. Rotation parameter is found to stabilize the system significantly.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0268-4
      Issue No: Vol. 25, No. 2 (2017)
  • Parameter-Robust Numerical Method for Time-Dependent Weakly Coupled Linear
           System of Singularly Perturbed Convection-Diffusion Equations
    • Authors: S. Chandra Sekhara Rao; Varsha Srivastava
      Pages: 301 - 325
      Abstract: We present a parameter-robust numerical method for a time-dependent weakly coupled linear system of singularly perturbed convection-diffusion equations. A small perturbation parameter multiplies the second order spatial derivative in all the equations. The proposed numerical method uses backward Euler method in time direction on an uniform mesh together with a suitable combination of HODIE scheme and the central difference scheme in spatial direction on a Shishkin mesh. It is proved that the numerical method is parameter-robust of first order in time and almost second order in space. Numerical results are given in support of theoretical findings.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-016-0282-1
      Issue No: Vol. 25, No. 2 (2017)
  • Numerical Treatment for the Class of Time Dependent Singularly Perturbed
           Parabolic Problems with General Shift Arguments
    • Authors: Komal Bansal; Pratima Rai; Kapil K. Sharma
      Pages: 327 - 346
      Abstract: In this paper we design two numerical schemes for solving a class of time dependent singularly perturbed parabolic convection–diffusion problems with general shift arguments in the reaction term. The discretization in both the directions is based on finite difference scheme. Special type of mesh and interpolation is used to tackle the terms containing shifts. The earlier numerical schemes for the considered problem are restricted to the case of small delay and advance arguments while in practical situations these shift arguments can be of arbitrary size (i.e., may be big or small enough in size). In this paper we propose two numerical schemes which work in both the situations i.e., when shifts are big or small enough in size. An extensive amount of analysis is presented to show the linear convergence in space and time of both the schemes. Some numerical results are given to confirm the predicted theory and to show the effect of shifts on the solution.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0265-7
      Issue No: Vol. 25, No. 2 (2017)
  • Numerical Approximation of an Elastic Wave Model
    • Authors: Samir Kumar Bhowmik; Abdullah Aljouiee
      Pages: 361 - 371
      Abstract: Wave operators play an important role modeling various physical, engineering and biological problems. We consider an initial boundary value problem modeling an elastic wave propagation. We approximate the model using a Legendre spectral Galerkin method for the spatial approximation. We analyze the accuracy of such a spatial approximation. We perform some numerical experiments to demonstrate the scheme.
      PubDate: 2017-04-01
      DOI: 10.1007/s12591-015-0254-x
      Issue No: Vol. 25, No. 2 (2017)
  • Asymptotic Stability of Neutral Impulsive Stochastic Partial Differential
           Equation of Sobolev Type with Poisson Jumps
    • Authors: Alka Chadha; Swaroop Nandan Bora
      Abstract: This paper is concerned with the p-th asymptotical stability of the mild solution of an impulsive neutral stochastic integro-differential equation of Sobolev type involving Poisson jumps and non-instantaneous impulses. By utilizing Leray–Schauder fixed point theorem and compact semigroup, a set of sufficient conditions establishing the asymptotical stability of the mild solution to stochastic system in the p-moment is derived. An example is also considered for illustrating abstract results.
      PubDate: 2017-06-19
      DOI: 10.1007/s12591-017-0371-9
  • High-Order Compact Finite Difference Scheme for Pricing Asian Option with
           Moving Boundary Condition
    • Authors: Kuldip Singh Patel; Mani Mehra
      Abstract: In this paper, an unconditionally stable compact finite difference scheme for the solution of linear convection–diffusion equation is proposed. In the proposed scheme, second derivative approximations of the unknowns are eliminated with the unknowns itself and their first derivative approximations while retaining the fourth order accuracy and tri-diagonal nature of the scheme. Proposed compact finite difference scheme which is fourth order accurate in spatial variable and second or lower order accurate in temporal variable depending on the choice of weighted time average parameter is applied to Asian option partial differential equation. A diagonally dominant system of linear equation is obtained from the proposed scheme which can be efficiently solved. Two numerical examples are given to demonstrate the efficiency and accuracy of the proposed compact finite difference scheme.
      PubDate: 2017-06-15
      DOI: 10.1007/s12591-017-0372-8
  • On the Stability of First Order PDEs Associated to Vector Fields
    • Authors: Maysam Maysami Sadr
      Abstract: Let \(\mathcal {M}\) be a manifold, \(\mathcal {V}\) be a vector field on \(\mathcal {M}\) , and \(\mathcal {B}\) be a Banach space. For any fixed function \(f:\mathcal {M}\rightarrow \mathcal {B}\) and any fixed complex number \(\lambda \) , we study Hyers–Ulam stability of the global differential equation \(\mathcal {V}y=\lambda y+f\) .
      PubDate: 2017-06-13
      DOI: 10.1007/s12591-017-0369-3
  • Global Asymptotical Stability for a Diffusive Predator-Prey Model with
           Ratio-Dependent Holling Type III Functional Response
    • Authors: Wensheng Yang; Xuepeng Li
      Abstract: A diffusive predator–prey model with ratio-dependent Holling type III functional response is considered in this work. Sufficient conditions for the global asymptotical stability of the constant positive steady-state solution are derived by constructing recurrent sequences and using an iterative method. It is shown that our result supplements one of the main results of Shi and Li’s paper (Global asymptotic stability of a diffusive predator–prey model with ratio-dependent functional response. Appl Math Comput 250:71–77, 2015).
      PubDate: 2017-06-12
      DOI: 10.1007/s12591-017-0370-x
  • On Iterative Solutions and Error Estimations of a Coupled System of
           Fractional Order Differential-Integral Equations with Initial and Boundary
    • Authors: Hasib Khan; Hossein Jafari; Dumitru Baleanu; Rahmat Ali Khan; Aziz Khan
      Abstract: The study of boundary value problems (BVPs) for fractional differential–integral equations (FDIEs) is extremely popular in the scientific community. Scientists are utilizing BVPs for FDIEs in day life problems by the help of different approaches. In this paper, we apply monotone iterative technique for the existence, uniqueness and the error estimations of solutions for a coupled system of BVPs for FDIEs of orders \(\omega ,\epsilon \in \left( 3,4 \right] \) . The coupled system is given by $$\begin{aligned} D^{\omega }u\left( t \right)= & {} -G_1 \left( {t,I^{\omega }u\left( t \right) ,I^{\varepsilon }v\left( t \right) } \right) ,\\ D^{\varepsilon }v\left( t \right)= & {} -G_2 \left( {t,I^{\omega }u\left( t \right) ,I^{\varepsilon }v\left( t \right) } \right) ,\\ D^{\delta }u\left( 1 \right)= & {} 0=I^{3-\omega }u\left( 0 \right) =I^{4-\omega }u\left( 0 \right) , u(1)=\frac{{\Gamma }\left( {\omega -\delta } \right) }{{\Gamma }\left( \omega \right) }I^{\omega -\delta }\\&\quad G_1 \left( {t,I^{\omega }u\left( t \right) ,I^{\varepsilon }v\left( t \right) } \right) \left( {t=1} \right) ,\\ D^{\nu }v\left( 1 \right)= & {} 0=I^{3-\varepsilon }v\left( 0 \right) =I^{4-\nu }v\left( 0 \right) , v(1)=\frac{{\Gamma }\left( {\varepsilon -\nu } \right) }{{\Gamma }\left( \varepsilon \right) }I^{\varepsilon -\nu }\\&\quad G_2 \left( {t,I^{\omega }u\left( t \right) ,I^{\varepsilon }v\left( t \right) } \right) \left( {t=1} \right) , \end{aligned}$$ where \(t\in \left[ {0,1}\right] \) , \(\delta ,\nu \in \left[ {1,2} \right] .\) The functions \(G_1 ,G_2 :\left[ {0,1} \right] \times R\times R\rightarrow R,\) satisfy the Caratheodory conditions. The fractional derivatives \(D^{\omega },D^{\varepsilon },D^{\delta },D^{\nu }\) are in Riemann-Liouville sense and \(I^{\omega },I^{\varepsilon },I^{3-\omega },I^{4-\omega },I^{3-\varepsilon },I^{4-\varepsilon },I^{\omega -\delta },I^{\varepsilon -\nu }\) are fractional order integrals. The assumed technique is a better approach for the existence, uniqueness and error estimation. The applications of the results are examined by the help of examples.
      PubDate: 2017-06-08
      DOI: 10.1007/s12591-017-0365-7
  • Existence of Solutions of Impulsive Anti-periodic Type Boundary Value
           Problems for Singular Fractional Differential Systems
    • Authors: Yuji Liu
      Abstract: Results on the existence of solutions to a new class of impulsive singular fractional differential systems with multiple base points are established. The assumptions imposed on the nonlinearities, see (D1) and (D2) in Theorem 3.1, are weaker than known ones, (i.e., (A) in Introduction section). The analysis relies on a well known fixed point theorem. An example is given to illustrate the efficiency of the main theorems.
      PubDate: 2017-06-08
      DOI: 10.1007/s12591-017-0368-4
  • Traveling Wave Solutions to Kawahara and Related Equations
    • Authors: Stefan C. Mancas
      Abstract: Traveling wave solutions to Kawahara equation (KE), transmission line (TL), and Korteweg–de Vries (KdV) equation are found by using an elliptic function method which is more general than the \(\mathrm {tanh}\) -method. The method works by assuming that a polynomial ansatz satisfies a Weierstrass equation, and has two advantages: first, it reduces the number of terms in the ansatz by an order of two, and second, it uses Weierstrass functions which satisfy an elliptic equation for the dependent variable instead of the hyperbolic tangent functions which only satisfy the Riccati equation with constant coefficients. When the polynomial ansatz in the traveling wave variable is of first order, the equation reduces to the KdV equation with only a cubic dispersion term, while for the KE which includes a fifth order dispersion term the polynomial ansatz must necessary be of quadratic type. By solving the elliptic equation with coefficients that depend on the boundary conditions, velocity of the traveling waves, nonlinear strength, and dispersion coefficients, in the case of KdV equation we find the well-known solitary waves (solitons) for zero boundary conditions, as well as wave-trains of cnoidal waves for nonzero boundary conditions. Both solutions are either compressive (bright) or rarefactive (dark), and either propagate to the left or right with arbitrary velocity. In the case of KE with nonzero boundary conditions and zero cubic dispersion, we obtain cnoidal wave-trains which represent solutions to the TL equation. For KE with zero boundary conditions and all the dispersion terms present, we obtain again solitary waves, while for KE with all coefficients present and nonzero boundary condition, the solutions are written in terms of Weierstrass elliptic functions. For all cases of the KE we only find bright waves that are propagating to the right with velocity that is a function of both dispersion coefficients.
      PubDate: 2017-06-06
      DOI: 10.1007/s12591-017-0367-5
  • Propagation of Bursting Oscillations in Coupled Non-homogeneous
           Hodgkin–Huxley Reaction–Diffusion Systems
    • Authors: B. Ambrosio; M. A. Aziz-Alaoui; A. Balti
      Abstract: In this paper, we consider networks of reaction–diffusion systems of Hodgkin–Huxley type. We give a general mathematical framework, in which we prove existence and unicity of solutions as well as the existence of invariant regions and of the attractor. Then, we illustrate some relevant numerical examples and exhibit bifurcation phenomena and propagation of bursting oscillations through one and two coupled non-homogeneous systems.
      PubDate: 2017-06-01
      DOI: 10.1007/s12591-017-0366-6
  • Particular Solution of Linear Sequential Fractional Differential equation
           with Constant Coefficients by Inverse Fractional Differential Operators
    • Authors: Sanaa L. Khalaf; Ayad R. Khudair
      Abstract: This paper adopts the inverse fractional differential operator method for obtaining the explicit particular solution to a linear sequential fractional differential equation, involving Jumarie’s modification of Riemann–Liouville derivative, with constant coefficient s. This method depends on the classical inverse differential operator method and it is independent of the integral transforms. Several examples are then given to demonstrate the validity of our main results.
      PubDate: 2017-05-29
      DOI: 10.1007/s12591-017-0364-8
  • Fitted Numerical Methods for Singularly Perturbed One-Dimensional
           Parabolic Partial Differential Equations with Small Shifts Arising in the
           Modelling of Neuronal Variability
    • Authors: R. Nageshwar Rao; P. Pramod Chakravarthy
      Abstract: In this paper, we presented exponentially fitted finite difference methods for a class of time dependent singularly perturbed one-dimensional convection diffusion problems with small shifts. Similar boundary value problems arise in computational neuroscience in determination of the behavior of a neuron to random synaptic inputs. When the shift parameters are smaller than the perturbation parameter, the shifted terms are expanded in Taylor series and an exponentially fitted tridiagonal finite difference scheme is developed. The proposed finite difference scheme is unconditionally stable and is convergent with order \(O(\Delta t+h^{2})\) where \(\Delta t\) and h respectively the time and space step-sizes. When the shift parameters are larger than the perturbation parameter a special type of mesh is used for the space variable so that the shifts lie on the nodal points and an exponentially fitted scheme is developed. This scheme is also unconditionally stable. By means of two examples, it is shown that the proposed methods provide uniformly convergent solutions with respect to the perturbation parameter. On the basis of the numerical results, it is concluded that the present methods offer significant advantage for the linear singularly perturbed partial differential difference equations.
      PubDate: 2017-05-09
      DOI: 10.1007/s12591-017-0363-9
  • On Inverse Full State Hybrid Function Projective Synchronization For
           Continuous-time Chaotic Dynamical Systems with Arbitrary Dimensions
    • Authors: Adel Ouannas; Ahmad Taher Azar; Toufik Ziar
      Abstract: Referring to continuous-time chaotic dynamical systems, this paper investigates the inverse full state hybrid function projective synchronization (IFSHFPS) of non-identical systems characterized by different dimensions. By taking a master system of dimension n and a slave system of dimension m, the method enables each master system state to be synchronized with a linear combination of slave system states, where the scaling factor of the linear combination can be any arbitrary differentiable function. The approach, based on the Lyapunov stability theory and stability of linear continuous-time systems, presents some useful features: (i) it enables non-identical chaotic systems with different dimension \(n<m\) or \(n>m\) to be synchronized; (ii) it can be applied to a wide class of chaotic (hyperchaotic) systems for any differentiable scaling function; (iii) it is rigorous, being based on two theorems, one for the case \(n<m\) and the other for the case \(n>m\) . Two different numerical examples are reported. The examples clearly highlight the capability of the conceived approach in effectively achieving synchronized dynamics for any differentiable scaling function.
      PubDate: 2017-04-27
      DOI: 10.1007/s12591-017-0362-x
  • Uniformly Convergent Second Order Numerical Method for a Class of
           Parameterized Singular Perturbation Problems
    • Authors: D. Shakti; J. Mohapatra
      Abstract: In this article, a class of nonlinear singularly perturbed boundary value problems depending on a parameter are considered. To solve this class of problems; first we apply the backward Euler finite difference scheme on Shishkin type meshes [standard Shishkin mesh (S-mesh), Bakhvalov–Shishkin mesh (B–S-mesh)]. The convergence analysis is carried out and the method is shown to be convergent with respect to the small parameter and is of almost first order accurate on S-mesh and first order accurate on B–S-mesh. Then, to improve the accuracy of the computed solution from almost first order to almost second order on S-mesh and from first order to second order on B–S-mesh, the post-processing method namely, the Richardson extrapolation technique is applied. The proof for the uniform convergence of the proposed method is carried out on both the meshes. Numerical experiments indicate the high accuracy of the proposed method.
      PubDate: 2017-04-24
      DOI: 10.1007/s12591-017-0361-y
  • The Well-Posedness of Fractional Systems with Affine-Periodic Boundary
    • Authors: Fei Xu; Yong Li; Yixian Gao; Xu Xu
      Abstract: This paper is devoted to study the existence and uniqueness of solutions for a class of nonlinear fractional dynamical systems with affine-periodic boundary conditions. We can show that there exists a solution for an \(\alpha \) -fractional system via the homotopy invariance of Brouwer degree, where \(0<\alpha \le 1\) . Furthermore, using Gronwall–Bellman inequality, we can prove the uniqueness of the solution if the nonlinearity satisfies the Lipschitz continuity. We apply the main theorem to the fractional kinetic equation and fractional oscillator with constant coefficients subject to affine-periodic boundary conditions. And in appendix, we give the proof of the nonexistence of affine-periodic solution to a given \((\alpha ,Q,T)\) -affine-periodic system in the sense of Riemann–Liouville fractional integral and Caputo derivative for \(0<\alpha <1\) .
      PubDate: 2017-04-08
      DOI: 10.1007/s12591-017-0360-z
  • Well-Posedness for a System of Integro-Differential Equations
    • Authors: Irene Benedetti; Luca Bisconti
      Abstract: We give sufficient conditions for the existence, the uniqueness and the continuous dependence on initial data of the solution to a system of integro-differential equations with superlinear growth on the nonlinear term. As possible applications of our methods we consider two epidemic models: a perturbed versions of the well-known integro-differential Kendall SIR model, and a SIRS-like model.
      PubDate: 2017-04-04
      DOI: 10.1007/s12591-017-0359-5
  • Editorial
    • Authors: Kapil K. Sharma; R. K. Mohanty
      PubDate: 2017-02-07
      DOI: 10.1007/s12591-017-0347-9
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