الفهرس 
History of Fractional Calculus
Approximate Methods Applied forOnly 14 pages are availabe for public view
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Abstract
Integral equations (IEs) are of high applicability in di¤erent areas of ap- plied Mathematics, Physics, and Engineering. In particular, they are widely used in Mechanics, electricity and magnetism, kinetic theory of gases, quantum mechanics, mathematical economics and queuing theory. An e¤ective and easy-to-use method for solving such equations is needed, in this work, we are concerning with two analytical methods; the classical method of successive approximations (Picard method) which consists of the construc- tion of a sequence of functions such that the limit of this sequence of functions in the sense of uniform convergence is the solution of integral equation of frac- tional order, and Adomian method which gives the solution as a series and the numerical method predictor corrector method for an initial value problem of arbitrary fractional orders integral equation. The existence and uniqueness of the solution and the convergence will be discussed for each method A comparative study of Picard, Adomian and Predictor-Corrector methods is presented for integral equations of fractional order and Coupled systems of these equations. Also, some numerical examples are discussed by MATHEMATICA package to compare the maximum error for each method.