الفهرس 
AcknowledgmentOnly 14 pages are availabe for public view
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Abstract
In this thesis, the optima homotopy analysis method (OHAM) is used to solve nonlinear fractional partial differential equations (FPDEs). Two main kinds of equations are discussed. The first kind includes the diffusion equation and the wave equation, while the second a higher order nonlinear FPDEs, precisely fourth order equations. The FPDEs with spatial second derivative is replaced by Riesz-Feller fractional derivative and in case of fourth derivative the Riesz-Feller operator is applied repeatedly. The continuation of the solution when the Riesz-Feller fractional derivative parameter approaches the integer order case is proved via two theorems, considering the diffusion and the wave problems. However, some nonlinear examples of FPDEs are presented to prove the continuation numerically. This thesis consists of five chapters and in the following we give a brief summary of each chapter. Chapter 1 : In this chapter, a brief history of FC is given along with a summary of the main definitions of fractional derivatives and their properties. The optimal homotopy analysis method (OHAM) and its application for solving fractional differential equations (FDEs) and fractional partial differential equations (FPDEs) are illustrated. Chapter 2 : In this chapter we aim to establish the continuation of the solution of the linear form of a fractional diffusion equation to the exact solution of the corresponding equation in Riesz fractional derivative as the skewness parameter approaches zero, i.e., θ→0. This objective is carried out theoretically using the Lebesgue dominated convergence theorem Chapter 3 : In this chapter, we prove the continuation of the solution of a space-time fractional order wave equation with spatial derivative in Reisz-Feler sense and Caputo derivative in time to the exact solution of the corresponding integer-order equation as the order of the fractional derivative approaches its integer limit. This objective is carried out theoretically then via approximate series solution obtained iteratively by applying the OHAM. Chapter 4 : In this chapter we give a recipe for obtaining the analytic approximate solution of the unified time-space fractional equation of order four. This class of equations include the SH, the EFK and the KS equations Chapter 5 : In this chapter a brief conclusion to the work is given with emphasis on the main results. Then the chapter is ended with some open points of future work.