Generalized Spline Approach For Solving System of Linear Fractional Volterra Integro-Differential Equations

Nabaa Najdi Hasan,Doaa Ahmed Hussien

doi:10.30526/31.1.1842

Abstract

In this paper generalized spline method is used for solving linear system of fractional integro-differential equation approximately. The suggested method reduces the system to system of linear algebraic equations. Different orders of fractional derivative for test example is given in this paper to show the accuracy and applicability of the presented method.

Highlights

The concept of fractional or non-integer order derivative and integration can be traced back to the genesis of integer order calculus itself
Almost every mathematical theory applicable to the study of non-integer order calculus was developed through the end of 19th century
We present numerical solution of the system of integro-differential equation with fractional derivative

Summary

Introduction

The concept of fractional or non-integer order derivative and integration can be traced back to the genesis of integer order calculus itself. There are several approaches to the generalization of the notation of differentiation of fractional orders, e.g. Riemann-Liouville, Grunwald-Letnikov, Caputo and generalized functions approach [3]. We present numerical solution of the system of integro-differential equation with fractional derivative. Generalized spline function: Consider the linear differential operator, [4]:

Results

Conclusion