الفهرس 
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Abstract
The aim of the present thesis is to obtain a Lie symmetries, conservation laws and analytical solutions for some nonlinear fractional partial differential equations. So, we use the Lie symmetry analysis to detect the symmetries for some nonlinear fractional partial differential equations. Also, we apply a set of analytical and numerical methods to construct a new solutions for these equations. Add to that, we derive the conservation laws for these equations by using the new conservation laws theorem and the formal Lagrange L. This thesis is organized as follow: Chapter 1.
In this chapter, we display an introduction about the fractional calculus which is a branch of mathematics, that investigates the properties of non-integer order derivatives and integrals (also they are known as fractional derivatives and integrals, or for short differintegrals). This discipline is especially interested in the concepts and methods for solving differential equations involving fractional derivatives of an unknown function. The history of fractional calculus began almost at the same time with that of classical calculus. It was first mentioned in Leibniz’s 1695 letter to L’Hopital, where the concept of semiderivative was proposed. He inquired about dxn , which is Leibniz’s notation for the nth derivative of the linear function f(x) = x. L’Hopital was intrigued and inquired as to what would happen
if n = 2. According to Leibniz, it would be “an apparent paradox, from which one day useful consequences will be drawn”. That date is considered to be the fractional calculus’s exact birthday. After that, we display the development, applications, and preliminaries of fractional calculus which include functions and theorems of this branch of mathematics. Moreover, we explain the description of Lie symmetry analysis for the non-linear fractional partial differential equations (NLFPDEs), provided with showing how to detect the sym-metries for these equations. In addition, we introduce the preliminaries of the conservation laws with investigating the conservation laws equation for the NLFPDEs. Also, this chapter includes some basic definitions, functions, and theorems which have been appeared in the field of fractional calculus. Furthermore, we display some powerful methods which have been used to build analytical and numerical solutions for some NLFPDEs.