Ghenaiet, Bahia2022-08-312022-08-312022http//localhost:8080/jspui/handle/123456789/5086In 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.enFractional differential equation , Caputo fractional derivative, Series solution, Homotopy analysis methodThesis