International Journal of Differential Equations
 Journal metrics
Acceptance rate25%
Submission to final decision46 days
Acceptance to publication47 days
CiteScore1.900
Journal Citation Indicator0.520
Impact Factor-

Boundary Value Problem for the Langevin Equation and Inclusion with the Hilfer Fractional Derivative

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International Journal of Differential Equations publishes research on differential equations, and related integral equations, from all scientists who use differential equations as tools within their own discipline.

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Existence of Strong Solutions for Nonlinear Systems of PDEs Arising in Convective Flow

In this paper, we will study the existence of strong solutions for a nonlinear system of partial differential equations arising in convective flow, modeling a phenomenon of mixed convection created by a heated and diving plate in a porous medium saturated with a fluid. The main tools are Schäfer’s fixed-point theorem, the Fredholm alternative, and some theorems on second-order elliptic operators.

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Dynamics of Mosquito Population Models with Spatial Diffusion

In this paper, we study some reaction-diffusion models of interactive dynamics of the wild and sterile mosquitoes. The well-posedness of the concerned model is proved. The stability of the steady states is discussed. Numerical simulations are presented to illustrate our theoretical results.

Review Article

Analytical Solutions for the Equal Width Equations Containing Generalized Fractional Derivative Using the Efficient Combined Method

In this paper, the efficient combined method based on the homotopy perturbation Sadik transform method  (HPSTM) is applied to solve the physical and functional equations containing the Caputo–Prabhakar fractional derivative. The mathematical model of this equation of order with is presented as follows: where for and , equations are changed into the equal width and modified equal width equations, respectively. The analytical method which we have used for solving this equation is based on a combination of the homotopy perturbation method and Sadik transform. The convergence and error analysis are discussed in this article. Plots of the analytical results with three examples are presented to show the applicability of this numerical method. Comparison between the obtained absolute errors by the suggested method and other methods is demonstrated.

Research Article

The Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic Media

In this paper, we consider the reconstruction of heat field in one-dimensional quasiperiodic media with an unknown source from the interior measurement. The innovation of this paper is solving the inverse problem by means of two different homotopy iteration processes. The first kind of homotopy iteration process is not convergent. For the second kind of homotopy iteration process, a convergent result is proved. Based on the uniqueness of this inverse problem and convergence results of the second kind of homotopy iteration process with exact data, the results of two numerical examples show that the proposed method is efficient, and the error of the inversion solution is given.

Research Article

An Effective Solution of the Cube-Root Truly Nonlinear Oscillator: Extended Iteration Procedure

The cube-root truly nonlinear oscillator and the inverse cube-root truly nonlinear oscillator are the most meaningful and classical nonlinear ordinary differential equations on behalf of its various applications in science and engineering. Especially, the oscillators are used widely in the study of elastic force, structural dynamics, and elliptic curve cryptography. In this paper, we have applied modified Mickens extended iteration method to solve the cube-root truly nonlinear oscillator, the inverse cube-root truly nonlinear oscillator, and the equation of pendulum. Comparison is made among iteration method, harmonic balance method, He’s amplitude-frequency formulation, He’s homotopy perturbation method, improved harmonic balance method, and homotopy perturbation method. After comparison, we analyze that modified Mickens extended iteration method is more accurate, effective, easy, and straightforward. Also, the comparison of the obtained analytical solutions with the numerical results represented an extraordinary accuracy. The percentage error for the fourth approximate frequency of cube-root truly nonlinear oscillator is 0.006 and the percentage error for the fourth approximate frequency of inverse cube-root truly nonlinear oscillator is 0.12.

Research Article

Parameter-Uniform Numerical Scheme for Singularly Perturbed Delay Parabolic Reaction Diffusion Equations with Integral Boundary Condition

Numerical computation for the class of singularly perturbed delay parabolic reaction diffusion equations with integral boundary condition has been considered. A parameter-uniform numerical method is constructed via the nonstandard finite difference method for the spatial direction, and the backward Euler method for the resulting system of initial value problems in temporal direction is used. The integral boundary condition is treated using numerical integration techniques. Maximum absolute errors and the rate of convergence for different values of perturbation parameter and mesh sizes are tabulated for two model examples. The proposed method is shown to be parameter-uniformly convergent.

International Journal of Differential Equations
 Journal metrics
Acceptance rate25%
Submission to final decision46 days
Acceptance to publication47 days
CiteScore1.900
Journal Citation Indicator0.520
Impact Factor-
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