Analytical and approximate solutions of Fractional Partial Differential-Algebraic Equations

Hatıra Günerhan,Ercan Çelik

doi:10.2478/amns.2020.1.00011

Abstract

Abstract In this paper, we have extended the Fractional Differential Transform method for the numerical solution of the system of fractional partial differential-algebraic equations. The system of partial differential-algebraic equations of fractional order is solved by the Fractional Differential Transform method. The results exhibit that the proposed method is very effective.

Highlights

In the past several years ago, various methods have been proposed to obtain the numerical solution of partial differential-algebraic equations [2], [7], [11]- [16]
The purpose of this paper is to consider the numerical solution of FPDAEs by using Fractional Differential Transform Method
The generalized differential transformation method displayed in this work is an effective method for the numerical solution of a fractional partial differential-algebraic equation system

Summary

Introduction

In the past several years ago, various methods have been proposed to obtain the numerical solution of partial differential-algebraic equations [2], [7], [11]- [16]. We consider the following system of partial differential-algebraic equations of fractional order. ADαt v(t, x) + BLxv(t, x) +Cv(t, x) = f (t, x), Where αis a parameter describing the fractional derivative and t ∈ (0,te), 0 < α ≤ 1 and x ∈ (−l, l) ⊂ R, A, B,C ∈ Rn×n, are constant matrices, u, f : [0,te] × [−l, l] → Rn. The purpose of this paper is to consider the numerical solution of FPDAEs by using Fractional Differential Transform Method.

Basic Definitions

Numerical example

Conclusions