الفهرس 
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Abstract
The aim of the thesis is to discuss the effectiveness of invariant subspace method for solving partial differential equations. This method can be successfully used to find exact solution of nonlinear partial differential equations as well as nonlinear fractional partial differential equations. The thesis is organized in four chapters as follows: In chapter one, we have introduced an introduction of the invariant subspace method, the steps for determining the exact solutions of partial differential equations. Also, a brief introduction of the invariant subspace method for solving time fractional partial differential equations is introduced. Finally, we end chapter one with some definitions. In chapter two, the invariant subspace method is used to obtain exact solutions for the generalized nonlinear diffution-convection equation. In chapter three, the invariant subspace method is used to investigate some new exact solutions of some fractional PDEs. Also, we applied this method to get the exact solution of sequential fractional PDEs. In chapter four, concluding remarks and suggested future work are given.