Existence and Convergence Results for Caputo Fractional Volterra Integro-Differential Equations

Abstract

In this article, homotopy analysis method is successfully applied to find the approximate solution of Caputo fractional Volterra integro-differential equation. The reliability of the method and reduction in the size of the computational work give this method a wider applicability. Also, the behavior of the solution can be formally determined by analytical approximate. Moreover, we proved the existence and convergence of the solution. Finally, an example is included to demonstrate the validity and applicability of the proposed technique.

Laplace discrete decomposition method for solving nonlinear Volterra-Fredholm integro-differential equations

“…The integro-differential equations have attracted much more interest of mathematicians and physicists which provides an efficiency for the description of many practical dynamical arising in engineering and scientific disciplines such as, physics, biology, electrochemistry, chemistry, economy, electromagnetic, control theory and viscoelasticity [2,3,5,12,13,15,16,19,[21][22][23]. In recent years, many authors focus on the development of numerical and analytical techniques for fractional integro-differential equations.…”

New reliable modifications of HPM and HAM

“…In one of his pioneering articles, he claimed that the method does not require either small or large parameters comparing with the perturbation techniques. The general concept of this method has been considered by many researchers in their published works [1][2][3][4][5].…”

Solving FIDEs by Using Semi-Analytical Techniques

“…For example, it was applied to the quadratic Ricatti differential equation by Abbasbandy [3], to the axisymmetric flow over a stretching sheet by Ariel et al [4], to the Helmholtz equation and fifth-order KdV equation by Rafei and Ganji [5], for the thin film flow of a fourth grade fluid down a vertical cylinder by Siddiqui et al [6], to the non-linear Volterra-Fredholm integral equations by Hamoud and Ghadle [7], to FIDE [8], to system of Fredholm integral equations [9], Alao et al [10] studied the ADM and the VIM on various types of integro-differential equation. Moreover, many methods for solving integro-differential equations have been studied by several authors [11,12,13,14,15,16,17,18,19,20,21].…”