Solutions of Systems of Fractional Differential Equation

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Tanash, Khaled "Ahmmad Mahmoud". Solutions of Systems of Fractional Dif-
ferential Equations, Master of Science in Mathematics, Yarmouk University, 2008,
(Supervisor: Dr. Edris A. Rawashdeh).
In this thesis, the Adomian Decomposition Method is used to solve systems of
fractional di¤erential equations. The solutions are calculated in the form conver-
gent power series with easily computable components. The signi…cant of this work
is that the Decomposition Method reduces the number of computations, improves
the accuracy and yields convergence. The convergence of Adomian Decomposition
Method for systems of fractional di¤erential equations is discussed. Moreover, a
great deal of development is added to the Numerical method for approximating the
solution of systems of fractional di¤erential equations based on the Splines Collo-
cation Method. Numerical examples are provided to illustrate the main results.
Key Words: Fractional calculus, Numerical solutions, Fractional di¤erential
equation, Systems of Fractional Di¤erential equations, Adomian Decomposition
Method, Splines Collocation Method.