Numerical Solution of High-Order Fractional Volterra Integro-Differential Equations by Variational Homotopy Perturbation Iteration Method

Abstract

In this paper, variational homotopy perturbation iteration method (VHPIM) has been applied along with Caputo derivative to solve high-order fractional Volterra integro-differential equations (FVIDEs). The “VHPIM” is present in all two steps. In order to indicate the efficiency and simplicity of the proposed method, we have presented some examples. All of the numerical computations in this study have been done on a personal computer applying some programs written in Maple18.

A computational technique for the solution of high-order fractional Volterra integro-differential equations

“…Approximate result of test example 3.1. Let us now Consider the Volterra integro-differential equation [18]:…”

Fractional advection differential equation within Caputo and Caputo–Fabrizio derivatives

“…In equation (19), p 2 ½0, 1 is a secured parameter and u 0 is a primary estimate of formula (5). Balancing the sentences featuring the same powers of p in two sides of the formula (18), we may obtain u j ( j = 0, 1, 2, .…”

A reliable mixed method for singular integro-differential equations of non-integer order

“…Here in particular, there can be applications in the excitatory neurons, the activity of interacting inhibitory and electric-circuit analysis cited. Furthermore, checking of systems among viscoelastic material dynamics and floating structures is governed by FIDEs [14]. From a historical standpoint, the model is remarkable in the sense that it uses approximate solutions and phase plane manners to arithmetic for finding responses for various stimuli originating from neuronal populations.…”

“…This makes use of the approximate or numerical solution methods to support obtaining a solution to this problem. Using approximate or numerical solution methods in order to solve the FDEs, FIDEs and SFIBVPs has been proposed by the scholars who have recorded that including the following: homotopy analysis method and q-homotopy analysis method [1,4], variational iteration method [2,13], Adomian's decomposition method [2], homotopy perturbation method and optimal homotopy perturbation method [13,20,23] and collocation method [6,25] and so on [9,14,26].…”