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Solution of fractional differential equations by using differential transform method. (English) Zbl 1152.34306
Summary: We implement a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equations. Theorems that never existed before are introduced with their proofs. Also numerical examples are carried out for various types of problems, including the Bagley-Torvik, Riccati and composite fractional oscillation equations for the application of the method. The results obtained are in good agreement with the existing ones in open literature and it is shown that the technique introduced here is robust, accurate and easy to apply.

##### MSC:
 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 26A33 Fractional derivatives and integrals 45D05 Volterra integral equations
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##### References:
  Ahmad WM, El-Khazali R. Fractional-order dynamical models of love. Chaos, Solitons & Fractals, in press, doi:10.1016/j.chaos.2006.01.098. · Zbl 1133.91539  Podlubny, I., Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications, (1999), Academic Press New York · Zbl 0924.34008  Caputo, M., Linear models of dissipation whose Q is almost frequency independent. part II, J roy austral soc, 13, 529-539, (1967)  Momani, S.; Odibat, Z., Numerical comparison of methods for solving linear differential equations of fractional order, Chaos, solitons & fractals, 31, 1248-1255, (2007) · Zbl 1137.65450  Shawagfeh, N.T., Analytical approximate solutions for nonlinear fractional differential equations, Appl math comput, 131, 517-529, (2002) · Zbl 1029.34003  Momani S, Shawagfeh N. Decomposition method for solving fractional Riccati differential equations. Appl Math Comput, in press, doi:10.1016/j.amc.2006.05.008. · Zbl 1107.65121  Momani, S.; Odibat, Z., Analytical approach to linear fractional partial differential equations arising in fluid mechanics, Phys lett A, 355, 271-279, (2006) · Zbl 1378.76084  Jumarie, G., Fractional Brownian motions via random walk in the complex plane and via fractional derivative. comparison and further results on their fokker – planck equations, Chaos, solitons & fractals, 22, 907-925, (2004) · Zbl 1068.60053  Benghorbal MM. Power series solution of fractional differential equations and symbolic derivatives and integrals. PhD thesis, The University of Western Ontario, London, Ontorio, 2004.  Arikoglu, A.; Ozkol, I., Solution of boundary value problems for integro-differential equations by using differential transform method, Appl math comput, 168, 1145-1158, (2005) · Zbl 1090.65145  Arikoglu, A.; Ozkol, I., Solution of difference equations by using differential transform method, Appl math comput, 174, 442-454, (2006)  Arikoglu A, Ozkol I. Solution of differential-difference equations by using differential transform method. Appl Math Comput, in press, doi:10.1016/j.amc.2006.01.022. · Zbl 1148.65310  Diethelm, K.; Ford, N.J., Numerical solution of the bagley – torvik equation, Bit, 42, 490-507, (2004) · Zbl 1035.65067  El-Mesiry, A.E.M.; El-Sayed, A.M.A.; El-Saka, H.A.A., Numerical methods for multi-term fractional (arbitrary) orders differential equations, Appl math comput, 160, 683-699, (2005) · Zbl 1062.65073  Diethelm, K.; Ford, N.J., Analysis of fractional differential equations, J math anal appl, 265, 229-248, (2002) · Zbl 1014.34003
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