Afrika Matematika

, Volume 30, Issue 7–8, pp 1133–1143

# Exact solution for the fractional partial differential equation by homo separation analysis method

• M. Zuriqat
Article

## Abstract

In this paper, the homo separation analysis method is used to obtain the exact solution for linear and nonlinear fractional partial differential equation (FPDE). This analytical method is a combination of the homotopy analysis method with the separation of variables method. By using this method, FPDE to be solved is changed into FODE. However, this method depends on several important topics and definitions such as Riemann–Liouville fractional integral, Caputo’s definition and Mittag-leffler function. In order to illustrate the simplicity and ability of the suggested approach, some specific and clear examples have been given.

## Keywords

Homotopy analysis method Separation of variables Partial differential equations Mittag-leffler function Caputo derivative Relaxation–oscillation equation

35M11

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