الفهرس 
Chapter I: IntroductionOnly 14 pages are availabe for public view
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Abstract
The aim of this thesis is to obtain exact solutions for some systems of nonlinear partial fractional differential equations (NLPFDEs), which play an important role for understanding of qualitative as well as quantitative features of many phenomena and processes in mathematical physics. Many studies have implied that the fractional phenomena is related with not only the pure mathematics, but also the applied sciences such as fluid mechanics, arterial mechanics, optical fibers, geochemistry, plasma physics, ... etc. Obtaining exact solutions for some NLPFDEs make it possible to understand the mechanism of complex nonlinear effects.
There are many methods to find exact solutions for nonlinear partial differentia equations such as: the sub-equation method, the exp-function method, the F-expansion method, the tanh-function method, the Ba ̈cklund transformation method, the Riccati expansion method, the first integer method, ... etc. In our study we use the following methods: the modified extended direct algebraic method, the improved (G’/G)-expansion method, the two variables (G’/G, 1/G)-expansion method, the (1/G’)-expansion method and the modified Kudryashov method. We have used these methods to obtain analytic solutions for the space-time fractional of classical Drinfeld Sokolov-Wilson (DSW) system, the fractional (2 1)-dimensional Davey-Stewartson (DS) system and the fractional Hirota-Satsuma (HS) coupled Korteweg-de Vries (KdV) system. Firstly, we use fractional traveling wave transformations to convert NLPFDEs into ordinary differential equations. Afterwards, the methods mentioned above have been implemented and several classes of solitary wave solutions are obtained for the above mentioned systems. The obtained solutions are expressed by the hyperbolic functions, the trigonometric functions and/or the rational functions. We also report here that some of our obtained solutions are new and the others are well known, thought, they obtained by different methods.