About solutions of fractional partial differential equations

Abstract

In this thesis, we present an optimal homotopy analysis method to obtain approximate solution for partial differential equation of fractional order. This method was applied to obtain a numerical solution of time-fractional hyperbolic partial differential equation.

Another method called the optimal homotopy asymptotic method was applied to get the approximate analytic solutions for two strongly fractional-order nonlinear benchmark oscillatory problems.

As a result, these methods allow us to control the convergent region of the series solution. Some numerical examples are presented to prove the accuracy of the method.