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|Title:||About solutions of fractional partial differential equations|
|Keywords:||Fractional differential equation , Caputo fractional derivative, Series solution, Homotopy analysis method|
|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.|
|Appears in Collections:||3.Faculté des Science Exactes et des Sciences de la Nature et de la Vie(temp)|
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