Fractional power series method for solving fractional differemtial equation

Runqing Cui,Yue Hu

doi:10.24297/jam.v12i4.360

Abstract

we use fractional power series method (FPSM) to solve some linear or nonlinear fractional differential equations . Compared to the other method, the FPSM is more simple, derect and effective.

Highlights

Many phenomena in applied sciences and engineering can be decribed successfully by using fractional order differential equation [1,2,3,4,5,6,7]
We consider the fractional Riccati equation that is frequently encountered in optimal control problem
we have the solution as u

Summary

Introduction

Many phenomena in applied sciences and engineering can be decribed successfully by using fractional order differential equation [1,2,3,4,5,6,7]. Fractional order differential equations are usually hard to solve analytically and exact solution are rather difficult to be obtained. It is very important to find efficient methods for solving these equations. Various researchers have introduced new methods in the literature. These methods include variational iteration method (VIM) [1], homotopy perturbation method (HPM) [2], homotopy analysis method (HAM) [3], DGJ method [5], Adomian decomposition method (ADM) [4], and other methods [7]. We will use fractional power series method (FPSM) [10] to solve some fractional differential equations.

Example 1

Example 2