الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The main objective of this work is to solve fractional-order partial differential equations using similarity method. Similarity method has been used because this method reduce the number of variables of the equation by one variable. We begin with fractional partial differential equation (FPDE) of two variables and reduce it to ordinary one. The ordinary differential equation obtained is solved by power series or by Fourier transform. First, we introduce similarity method for solving FPDEs with Caputo fractional derivative. In this part, we solve time-fractional diffusion equation with variable coefficients, space fractional diffusion equation with variable coefficients, multi-term time-fractional diffusion equation, and higher order FPDEs. For each problem we use similarity method to transform the considered FPDE into fractional ordinary differential equation and then find its solution using power series and test the convergence of the solution. The second type of FPDEs that we solve by similarity method is Riesz FPDEs. The resulting fractional ordinary differential equations are solved by Fourier transform method. Finally, we use similarity method for solving FPDEs with Riesz-Feller fractional derivative. The resulting fractional ordinary differential equations are solved by Fourier transform method.