Abstract: Abstract In this paper, we construct and implement a new improvement of third order weighted essentially non-oscillatory (WENO) scheme in the finite difference framework for hyperbolic conservation laws. In our approach, a modification in the global smoothness measurement is reported by applying all three points on global stencil \((i-1,i,i+1)\) which is used for convergence of non-linear weights towards the optimal weights at critical points and achieves the desired order of accuracy for third order WENO scheme. We use the third order accurate total variation diminishing (TVD) Runge-Kutta time stepping method. The major advantage of the proposed scheme is its better numerical accuracy in smooth regions. The computational performance of the proposed WENO scheme with this global smoothness measurement is verified in several benchmark one- and two-dimensional test cases for scalar and vector hyperbolic equations. Extensive computational results confirm that the new proposed scheme achieves better performance as compared with WENO-JS3, WENO-Z3 and WENO-F3 schemes. PubDate: 2019-12-03

Abstract: Abstract In this paper, we apply the reproducing kernel Hilbert space method (RKHSM) for solving third order differential equations with multiple characteristics in a rectangular domain. The exact solution is expressed in a series form. The numerical examples are given to demonstrate the good performance of the presented method. The results obtained indicate that the method is simple and effective. PubDate: 2019-11-30

Abstract: Abstract In this article, we introduce the new type of contractions for a mapping and a relation and prove certain coincidence point theorems which generalize some known results in this area. Moreover, an application to the existence of a unique solution for the integral equation is also provided. PubDate: 2019-11-28

Abstract: Abstract This article is about finding the possible solutions of fractional kinetic equation associated with the generalized multiindex Bessel function using the method of Laplace transform. Numerical results and graphical solutions of the main theorems are also presented. PubDate: 2019-11-21

Abstract: Abstract The role of astrocytes in physiological processes is always a matter of interest for biologists, mathematicians and computer scientists. Similar to neurons, astrocytes propagate Ca2+ over long distances in response to stimulation and release gliotransmitters in a Ca2+-dependent manner to modulate various important brain functions. There are various processes and parameters that affect the cytoplasmic calcium concentration level of astrocytes like calcium buffering, influx via calcium channels, etc. Buffers bind with calcium ion (Ca2+) and makes calcium bound buffers. Thus, it decreases the calcium concentration [Ca2+] level. Ca2+ enters into the cytosol through voltage gated calcium channel (VGCC) and thus it increases the concentration level. In view of above, a three-dimensional mathematical model is developed for combined study of the effect of buffer and VGCC on cytosolic calcium concentration in astrocytes. Finite element method is applied to find the solution using hexagonal elements. A computer programme is developed for entire problem to simulate the results. The obtained results show that high affinity buffer reveals the effect of VGCC and at low buffer concentration VGCC effects more significantly. PubDate: 2019-11-13

Abstract: Abstract In this article, we consider a nonlinear Sobolev type fractional functional integrodifferential equations in a Banach space along with a nonlocal condition. Sufficient conditions for existence, uniqueness and dependence on initial data of local solutions of considered problem are derived by employing fixed point techniques and theory of classical semigroup. Further, we also render the criteria for existence of global solution. At the end, we provide an application to elaborate the obtained results. PubDate: 2019-11-13

Abstract: Abstract In this paper, following Holly (Ann Polon Math LIV 2:93–109, 1991; Univ Iagell Acta Math XXXI:154–174, 1994), Holly and Motyl (Inversion of the \(divdiv^{\star }\)-operator and three numerical methods in hydrodynamics, selected Problems in Mathematics. Cracow University of Technology, pp 35–94, 1995) and Motyl (Univ Iagell Acta Math XXXVIII:227–277, 2000; Ann Fac Sci Toulouse XXI(4):651–743, 2012), we study stability of solutions from the perspective of Hausdorff metric. To be precise, we construct a sequence of sets of approximate solutions for stationary MHD equations by using Galerkin approximation method and prove that this sequence of sets converges to the set of actual solutions of stationary MHD equations. The convergence is with respect to Hausdorff metric which is a distance defined on a family of sets. PubDate: 2019-11-11

Abstract: Abstract We consider the population dynamics of prey under the effect of the two types of predators. One of the predator types is harvested, modelled with a term with a Michaelis–Menten type functional form. Besides local stability analysis, we are interested that how harvesting could directly affect the dynamics of the ecosystem, such as existence and dynamics of coexistence equilibria and periodic solutions. Theoretical and numerical methods are used to study the role played by several bifurcations in the mathematical models. PubDate: 2019-11-06

Abstract: Abstract The paper is concerned with the extension of a monotone iterative technique to impulsive finite delay differential equations of fractional order with a nonlocal initial condition in an ordered Banach space. We study the existence of extremal mild solutions with or without assuming the compactness of a semigroup and also prove the uniqueness of the mild solution of the system. The results are obtained with the help of fractional calculus, a measure of non-compactness, the semigroup theory and monotone iterative technique. Finally, an example is provided to show the application of our main. PubDate: 2019-10-29

Abstract: Abstract In this paper, the \(\psi \) -Riemann–Liouville fractional partial integral and the \(\psi \) -Hilfer fractional partial derivative are introduced and some of its particular cases are recovered. Using the Gronwall inequality and these results, we investigate the Ulam–Hyers and Ulam–Hyers–Rassias stabilities of the solutions of a fractional partial differential equation of hyperbolic type in a Banach space \(({\mathbb {B}}, \left \cdot \right )\) , real or complex. Finally, we present an example in order to elucidate the results obtained. PubDate: 2019-10-28

Abstract: Abstract In this work we give sufficient and necessary conditions for convergence for nonhyperbolic fixed points of dynamical systems of arbitrary dimension whose linearization around zero is the identity function. To achieve this goal, we first rewrite the dynamical system in terms of spherical polar coordinates and by approximation of the radial iteration function we discover a necessary condition depending on a remarkable angular function. Searching for conditions that are sufficient, we discover more angular functions that together with the first one gives a complete set that plays the role of the iteration derivative for unidimensional discrete systems. PubDate: 2019-10-28

Abstract: Abstract In this work, we investigate velocity magnetic particles by inextensible flows in sphere. We have advanced consequence of inextensible flows for velocity magnetic particles. Also, we characterize flows of electric field with Lorentz equation. Moreover, we get evolution equation of electric field in space. PubDate: 2019-10-08

Abstract: Abstract This paper is concerned with the following Kirchhoff-type equation $$\begin{aligned} -\left( a+b\int _{{\mathbb {R}}^3} \nabla u ^2dx\right) \varDelta u+V(x)u=Q(x)u^5+ f(x,u), \quad x \in {\mathbb {R}}^{3}, \end{aligned}$$ where \(a,b>0\) are constants, V(x), Q(x) and f(x, u) are periodic in x, and the nonlinear growth of \(u^5\) reaches the Sobolev critical exponent since \(2^*=6\) in dimension 3. Under some suitable assumptions on V, Q and f, using variational methods, we establish the existence of nontrivial ground state solution for the above equation. Recent results from the literature are improved and extended. PubDate: 2019-10-05

Abstract: Abstract In this work, we have discussed the oscillation properties of first order neutral impulsive difference equations with constant coefficients by using pulsatile constant. Also, we have made an effort to apply our constant coefficient results to nonlinear impulsive difference equations with variable coefficients. PubDate: 2019-10-03

Abstract: Abstract In this study, we deal with an inverse problem for Bessel operator on a finite interval. We present some results of the associated with Ambarzumyan’s theorem by using spectrum and nodal points (zeros of eigenfunction). PubDate: 2019-10-01

Abstract: Abstract I prove the bistability of linear evolution equations \(x'=A(t)x\) in a Banach space E, where the operator-valued function A is of the form \(A(t)=f'(t)G(t,f(t))\) for a binary operator-valued function G and a scalar function f. The constant that bounds the solutions of the equation is computed explicitly; it is independent of f, in a sense. Two geometric applications of the stability result are presented. Firstly, I show that the parallel transport along a curve \(\gamma \) in a manifold, with respect to some linear connection, is bounded in terms of the length of the projection of \(\gamma \) to a manifold of one dimension lower. Secondly, I prove an extendability result for parallel sections in vector bundles, thus answering a question by Antonio J. Di Scala. PubDate: 2019-10-01

Abstract: Abstract This paper investigates the problem of Q–S synchronization for different dimensional chaotic dynamical systems in discrete-time. Based on two control laws and stability theory of dynamical systems in discrete-time, new synchronization schemes are derived. Numerical examples demonstrate the effectiveness and feasibility of the proposed control techniques. PubDate: 2019-10-01

Abstract: Abstract We study the maximum number of limit cycles of the polynomial differential systems of the form $$\begin{aligned} \dot{x}=-y+l(x), \,\dot{y}=x-f(x)-g(x)y-h(x)y^{2}-d_{0}y^{3}, \end{aligned}$$ where \(l(x)=\varepsilon l^{1}(x)+\varepsilon ^{2}l^{2}(x),\) \(f(x)=\varepsilon f^{1}(x)+\varepsilon ^{2}f^{2}(x),\) \(g(x)=\varepsilon g^{1}(x)+\varepsilon ^{2}g^{2}(x),\) \(h(x)=\varepsilon h^{1}(x)+\varepsilon ^{2}h^{2}(x)\) and \(d_{0}=\varepsilon d_{0}^{1}+\varepsilon ^{2}d_{0}^{2}\) where \(l^{k}(x),\) \(f^{k}(x),\) \(g^{k}(x)\) and \(h^{k}(x)\) have degree m, \(n_{1},\) \(n_{2}\) and \(n_{3}\) respectively, \(d_{0}^{k}\ne 0\) is a real number for each \(k=1,2,\) and \(\varepsilon \) is a small parameter. We provide an upper bound of the maximum number of limit cycles that the above system can have bifurcating from the periodic orbits of the linear centre \(\dot{x}=-y,\, \dot{y}=x\) using the averaging theory of first and second order. PubDate: 2019-10-01

Abstract: Abstract We consider a Nicholson type system for two species with mutualism and nonlinear harvesting terms. We give sufficient conditions for the existence of a positive periodic solution. We also provide a necessary condition; more precisely, we prove that if the harvesting rate is large enough, then 0 is a global attractor for the positive solutions and, in particular, positive periodic solutions cannot exist. PubDate: 2019-10-01

Abstract: Abstract In this manuscript, we consider a nonlinear system governed by fractional differential equations in a Banach space. Used the semigroup theory of linear operators and Gronwal’s inequality to show the trajectory controllability of the system. Also, we extend our results to nonlocal and integro-differential equations. Finally, we give an example to illustrate the applications of these results. PubDate: 2019-10-01