Author:
Damak Mondher,Mohammed Zaid Amer
Abstract
Multidimensional integro-differential equations are obtained when the unknown function of several independent variable and/or its derivatives appear under an integral sign. When the differentiation or integration operators or both are of fractional order, the integral equation in this case is called a multidimensional fractional integro-differential equation. Such equations are difficult to solve analytically; therefore, as the main objective of this paper, an approximate method—which is the variational iteration method—will be used to solve this type of equation with conformable fractional-order derivatives and integrals. First, we drive the iterative sequence of approximate solutions using the proposed method, and then, under certain conditions over the kernel of the integro-differential equation, prove its convergence to the exact solution. Two illustrative examples, linear and nonlinear, are given, and their approximated solutions are simulated using computer programs in order to verify from the reliability and applicability of the proposed method.
Subject
Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis
Reference23 articles.
1. A theoretical basis for the application of fractional calculus to viscoelasticity;Bagley;J. Rheol.,1983
2. Almost sectorial operators on psi-Hilfer derivative fractional impulsive integro-differential equations;Karthikeyan;Math. Methods Appl. Sci.,2022
3. Variational Iteration Method for Solving Nonlinear Fractional Integro-Differential Equations;Kurulay;Int. J. Comput. Sci. Emerg. Technol.,2011
4. Variational Iteration Method for Solving Multi-Fractional Integro Differential Equations;Khaleel;J. Sci.,2014
5. Fang, J., Nadeem, M., Habib, M., and Akgül, A. Numerical Investigation of Nonlinear Shock Wave Equations with Fractional Order in Propagating Disturbance. Symmetry, 2022. 14.