Bessel Collocation Method for Solving Fredholm–Volterra Integro-Fractional Differential Equations of Multi-High Order in the Caputo Sense

Shazad Shawki Ahmed,Shabaz Jalil Mohammedfaeq

doi:10.3390/sym13122354

Abstract

The approximate solutions of Fredholm–Volterra integro-differential equations of multi-fractional order within the Caputo sense (F-VIFDEs) under mixed conditions are presented in this article apply a collocation points technique based completely on Bessel polynomials of the first kind. This new approach depends particularly on transforming the linear equation and conditions into the matrix relations (some time symmetry matrix), which results in resolving a linear algebraic equation with unknown generalized Bessel coefficients. Numerical examples are given to show the technique’s validity and application, and comparisons are made with existing results by applying this process in order to express these solutions, most general programs are written in Python V.3.8.8 (2021).

Highlights

Fractional calculus (FC) deals with the differentiation and integration of arbitrary order and it is used in the real world to model and analyze big problems
Several strategies for solving fractional order differential equations were presented for this purpose, [1,3,4]
We get the following system of equations by setting the collocation points, [28], dea scribed by xi = a + b−

Summary

Introduction

Fractional calculus (FC) deals with the differentiation and integration of arbitrary order and it is used in the real world to model and analyze big problems. Fractional differential equations and integro-fractional differential equations (IFDEs) have captivated the hobby of many researchers in various fields of science and era due to the reality that realistic modeling of a bodily phenomenon with dependencies in the immediate time, and in the past time history can be accomplished effectively using FC. In addition to modeling, the solution approaches and their dependability are crucial in detecting key points when a rapid divergence, convergence, or bifurcation begins. Several strategies for solving fractional order differential equations were presented for this purpose (or integro-differential equations), [1,3,4]. The Adomian decomposition method [5], variational iteration method [6], fractional differential transform method [7], fractional difference method [8], and power series method [9] are the most commonly used ideas

Objectives

Methods

Conclusion