الفهرس 
Some Properties of the Fractional DerivativesOnly 14 pages are availabe for public view
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Abstract
Fractional differential equations (FDEs) appear more and more frequently in various research areas and engineering applications including fluid flow, electrical networks, control theory, electromagnetic theory, optics, potential theory, biology, chemistry, probability, statistics, diffusion theory, fractals theory, electrochemistry, and viscoelasticity. An effective and easy-to-use method for solving such equations is needed. In this work, Adomian’s decomposition method (ADM) is used. This method solves successfully different types of linear and nonlinear FDEs and systems of such equations. ADM is applied to solve some applications such as the relaxation-oscillation equation, Basset problem, Riccati differential equation of fractional orders, and Abel integral equation. A comparative study between the solutions obtained by ADM with that solutions obtained by using some other methods such as Laplace transform method, fractional Green’s function, and numerical methods is done. A new approach for convergence of ADM when applied to system of nonlinear FDEs is introduced.