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 Advances in Difference Equations   [SJR: 0.647]   [H-I: 25]   [1 followers]  Follow       Open Access journal    ISSN (Print) 1687-1839 - ISSN (Online) 1687-1847    Published by SpringerOpen  [188 journals]
• A fractional order model for obesity epidemic in a non-constant population

• Abstract: Abstract In this paper, we propose a fractional order epidemic model for obesity contagion. The population size is assumed to be nonconstant, which is more realistic. The model considers vertical transmission of obesity and also obesity-related death rate. We give local stability analysis of the model. Finally, some numerical examples are presented.
PubDate: 2017-03-17

• A corresponding Cullen-regularity for split-quaternionic-valued functions

• Abstract: Abstract We give a representation of the class of Cullen-regular functions in split-quaternions. We consider each Cullen’s form of split-quaternions, which provides corresponding Cauchy-Riemann equations for split-quaternionic variables. Using Cullen’s form, we research hyperholomorphy and the properties of functions of split-quaternionic variables which are expressed by hyperbolic coordinates.
PubDate: 2017-03-17

• Dynamical analysis of the permanent-magnet synchronous motor chaotic
system

• Abstract: Abstract This paper is concerned with some dynamics of the permanent-magnet synchronous motor chaotic system based on Lyapunov stability theory and optimization theory. The innovation of the paper lies in that we derive a family of mathematical expressions of globally exponentially attractive sets for this chaotic system with respect to system parameters. Numerical simulations confirm that theoretical analysis results are correct.
PubDate: 2017-03-09

• Monotonicity results for fractional difference operators with discrete
exponential kernels

• Abstract: Abstract We prove that if the Caputo-Fabrizio nabla fractional difference operator $$({}^{\mathrm{CFR}}_{a-1}\nabla^{\alpha}y)(t)$$ of order $$0<\alpha\leq1$$ and starting at $$a-1$$ is positive for $$t=a,a+1,\ldots$$  , then $$y(t)$$ is α-increasing. Conversely, if $$y(t)$$ is increasing and $$y(a)\geq0$$ , then $$({}^{\mathrm{CFR}}_{a-1}\nabla^{\alpha}y)(t)\geq0$$ . A monotonicity result for the Caputo-type fractional difference operator is proved as well. As an application, we prove a fractional difference version of the mean-value theorem and make a comparison to the classical discrete fractional case.
PubDate: 2017-03-09

• Stability results for partial fractional differential equations with
noninstantaneous impulses

• Abstract: Abstract In this article, we investigate some uniqueness and Ulam’s type stability concepts for the Darboux problem of partial functional differential equations with noninstantaneous impulses and delay in Banach spaces. The main techniques rely on fractional calculus, integral equations and inequalities. Two examples are also provided to illustrate our results.
PubDate: 2017-03-09

• Stability results of a fractional model for unsteady-state fluid flow
problem

• Abstract: Abstract This paper mainly focuses on a fractional model for unsteady-state fluid flow problem developed based on the meshless local Petrov-Galerkin (MLPG) method with the moving kriging (MK) technique as a background. The contribution of this work is to investigate the stability of a model with fractional order governed by the full Navier-Stokes equations in Cartesian coordinate system both theoretical and numerical aspects. This is examined and discussed in detail by means of matrix method. We show that the scheme is unconditionally stable under the restriction of eigenvalue. The dependence between several of the important parameters that impact on the solution is also studied thoroughly. In discretizing the time domain, an algorithm based on a fixed point method is employed to overcome the nonlinearity. Two selected benchmark problems are provided to validate the stability of the present method, and a very satisfactory agreement with the obtained results can be found.
PubDate: 2017-03-09

• Approximation on the reciprocal-cubic and reciprocal-quartic functional
equations in non-Archimedean fields

• Abstract: Abstract The aim of this paper is to study the generalized Hyers-Ulam stability of a form of reciprocal-cubic and reciprocal-quartic functional equations in non-Archimedean fields. Some related examples for the singular cases of these new functional equations on an Archimedean field are indicated.
PubDate: 2017-03-09

• Two kinds of discrete integrable hierarchies of evolution equations and
some algebraic-geometric solutions

• Abstract: Abstract With the help of a loop algebra we first present a $$(1+1)$$ -dimensional discrete integrable hierarchy with a Hamiltonian structure and generate a $$(2+1)$$ -dimensional discrete integrable hierarchy, respectively. Then we obtain a new differential-difference integrable system with three-potential functions, whose algebraic-geometric solution is derived from the theory of algebraic curves, where we construct the new elliptic coordinates to straighten out the continuous and discrete flows by introducing the Abel maps as well as the Riemann-Jacobi inversion theorem.
PubDate: 2017-03-04

• A new operational matrix of Caputo fractional derivatives of Fermat
polynomials: an application for solving the Bagley-Torvik equation

• Abstract: Abstract Herein, an innovative operational matrix of fractional-order derivatives (sensu Caputo) of Fermat polynomials is presented. This matrix is used for solving the fractional Bagley-Torvik equation with the aid of tau spectral method. The basic approach of this algorithm depends on converting the fractional differential equation with its initial (boundary) conditions into a system of algebraic equations in the unknown expansion coefficients. The convergence and error analysis of the suggested expansion are carefully discussed in detail based on introducing some new inequalities, including the modified Bessel function of the first kind. The developed algorithm is tested via exhibiting some numerical examples with comparisons. The obtained numerical results ensure that the proposed approximate solutions are accurate and comparable to the analytical ones.
PubDate: 2017-03-04

• Asymptotic behavior of third-order functional differential equations with
a negative middle term

• Abstract: Abstract This paper is concerned with asymptotic and oscillatory properties of the nonlinear third-order differential equation with a negative middle term. Both delay and advanced cases of argument deviation are considered. Sufficient conditions for all solutions of a given differential equation to have property B or to be oscillatory are established. A couple of illustrative examples is also included.
PubDate: 2017-03-02

• A transfer theorem and stability of Levin-Nohel integro-differential
equations

• Abstract: Abstract In this paper we show a connection between Levin-Nohel integro-differential equations and ordinary functional differential equations. Based on this connection, we obtain several new conditions for the stability of the solution, including the famous 3/2 stability criterion.
PubDate: 2017-03-01

• Fractional optimal control problem for differential system with delay
argument

• Abstract: Abstract In this paper, we apply the classical control theory to a fractional differential system in a bounded domain. The fractional optimal control problem (FOCP) for differential system with time delay is considered. The fractional time derivative is considered in a Riemann-Liouville sense. We first study the existence and the uniqueness of the solution of the fractional differential system with time delay in a Hilbert space. Then we show that the considered optimal control problem has a unique solution. The performance index of a FOCP is considered as a function of both state and control variables, and the dynamic constraints are expressed by a partial fractional differential equation. The time horizon is fixed. Finally, we impose some constraints on the boundary control. Interpreting the Euler-Lagrange first order optimality condition with an adjoint problem defined by means of a right fractional Caputo derivative, we obtain an optimality system for the optimal control. Some examples are analyzed in detail.
PubDate: 2017-03-01

• The stable equilibrium of a system of piecewise linear difference
equations

• Abstract: Abstract In this article we consider the global behavior of the system of first order piecewise linear difference equations: $$x_{n+1} = \vert x_{n}\vert - y _{n} +b$$ and $$y_{n+1} = x_{n} - \vert y_{n}\vert - d$$ where the parameters b and d are any positive real numbers. We show that for any initial condition in $$R^{2}$$ the solution to the system is eventually the equilibrium, $$(2b + d, b)$$ . Moreover, the solutions of the system will reach the equilibrium within six iterations.
PubDate: 2017-02-28

• Existence of solutions for fractional stochastic impulsive neutral
functional differential equations with infinite delay

• Abstract: Abstract This paper addresses a class of fractional stochastic impulsive neutral functional differential equations with infinite delay which arise from many practical applications such as viscoelasticity and electrochemistry. Using fractional calculations, fixed point theorems and the stochastic analysis technique, sufficient conditions are derived to ensure the existence of solutions. An example is provided to prove the main result.
PubDate: 2017-02-28

• Homotopy perturbation transform method for nonlinear differential
equations involving to fractional operator with exponential kernel

• Abstract: Abstract This work presents the homotopy perturbation transform method for nonlinear fractional partial differential equations of the Caputo-Fabrizio fractional operator. Perturbative expansion polynomials are considered to obtain an infinite series solution. The effectiveness of this method is demonstrated by finding the exact solutions of the fractional equations proposed, for the special case when the limit of the integral order of the time derivative is considered.
PubDate: 2017-02-28

• A fourth-order accurate quasi-variable mesh compact finite-difference
scheme for two-space dimensional convection-diffusion problems

• Abstract: Abstract We discuss a new nine-point fourth-order and five-point second-order accurate finite-difference scheme for the numerical solution of two-space dimensional convection-diffusion problems. The compact operators are defined on a quasi-variable mesh network with the same order and accuracy as obtained by the central difference and averaging operators on uniform meshes. Subsequently, a high-order difference scheme is developed to get the numerical accuracy of order four on quasi-variable meshes as well as on uniform meshes. The error analysis of the fourth-order compact scheme is described in detail by means of matrix analysis. Some examples related with convection-diffusion equations are provided to present performance and robustness of the proposed scheme.
PubDate: 2017-02-27

• Stability and traveling waves in a Beddington-DeAngelis type
stage-structured predator-prey reaction-diffusion systems with nonlocal
delays and harvesting

• Abstract: Abstract The goal of this paper is to study the stability and traveling waves of stage-structured predator-prey reaction-diffusion systems of Beddington-DeAngelis functional response with both nonlocal delays and harvesting. By analyzing the corresponding characteristic equations, the local stability of various equilibria is discussed. We reduce the existence of traveling waves to the existence of a pair of upper-lower solutions by using the cross iteration method and the Schauder’s fixed point theorem. The existence of traveling waves connecting the zero equilibrium and the positive equilibrium is then established by constructing a pair of upper-lower solutions.
PubDate: 2017-02-27

• Oscillation criteria for difference equations with non-monotone arguments

• Abstract: Abstract This paper is concerned with the oscillatory behavior of first-order retarded [advanced] difference equation of the form $$\Delta x(n)+p(n)x\bigl(\tau (n)\bigr)=0, \quad n\in \mathbb{N} _{0} \qquad \bigl[\nabla x(n)-q(n)x\bigl(\sigma (n)\bigr)=0, \ n\in \mathbb{N} \bigr],$$ where $$(p(n))_{n\geq 0}$$ $$[(q(n))_{n\geq 1}]$$ is a sequence of nonnegative real numbers and $$\tau (n)$$ $$[\sigma (n)]$$ is a non-monotone sequence of integers such that $$\tau (n)\leq n-1$$ , for $$n\in \mathbb{N}_{0}$$ and $$\lim_{n\rightarrow \infty }\tau (n)=\infty$$ $$[\sigma (n)\geq n+1,\mbox{ for }n\in \mathbb{N}]$$ . Sufficient conditions, involving limsup, which guarantee the oscillation of all solutions are established. These conditions improve all previous well-known results in the literature. Also, using algorithms on MATLAB software, examples illustrating the significance of the results are given.
PubDate: 2017-02-27

• Systems of generalized Sturm-Liouville and Langevin fractional
differential equations

• Abstract: Abstract In this paper, we study anti-periodic boundary value problems for systems of generalized Sturm-Liouville and Langevin fractional differential equations. Existence and uniqueness results are proved via fixed point theorems. Examples illustrating the obtained results are also presented.
PubDate: 2017-02-27

• Sustained oscillation induced by time delay in a commodity market model

• Abstract: Abstract In this paper, the existence of local and global Hopf bifurcation for a delay commodity market model is studied in detail. As time delay increases, the commodity price will fluctuate periodically. Furthermore, such fluctuations will occur even if the time delay is sufficiently large.
PubDate: 2017-02-21

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