الفهرس 
Contemporary studiesOnly 14 pages are availabe for public view
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Abstract
Partial differential equations are used in describing a lot of systems and processes in various fields such as engineering, physics, economics,chemistry, biology, signal processing, control systems and so on of other sciences. It has been noticed that models with fractional order derivatives could describe precisely and accurately a lot of processes than their counterpart models with integer order derivatives.In this thesis, we introduce a numerical technique called exponential fitting for solving fractional partial differential equations FPDEs or distributed order fractional partial differential equations DOFPDEs types. The problems included in this thesis are distributed and constant order time fractional nonlinear reaction-diffusion equation,two-dimensional time fractional nonlinear damped Klein-Gordon equation and time fractional nonlinear Swift-Hohenberg equation (S-H).Firstly, we propose the time fractional derivative approximation methods in Caputo and Riemann-Liouville senses using different classes of weighted shifted Grünwald-Letnikov fractional derivative approximation. The six-step flow chart of the exponential fitting technique is proposed such that this flow chart will be adapted and developed for each type of time fractional partial differential equation in its own chapter. Exponential fitting technique depends on a free parameter that will be used to annihilate the leading term of the local truncation error and increase the accuracy of the proposed schemes.