Analytical approximate solutions for nonlinear fractional differential equations Nabil T. Shawagfeh 1 Department of Mathematics and Computer Science, Faculty of Science, United Arab Emirates University, P.O. Box 17551, Al-Ain, United Arab Emirates Abstract We consider a class of nonlinear fractional differential equations (FDEs) based on the Caputo fractional derivative and by extending the application of the Adomian de- composition method we derive an analytical solution in the form of a series with easily computable terms. For linear equations the method gives exact solution, and for non- linear equations it provides an approximate solution with good accuracy. Several ex- amples are discussed. Ó 2002 Elsevier Science Inc. All rights reserved. Keywords: Decomposition method; Fractional differential equation; Caputo fractional derivative; Adomian polynomials 1. Introduction Fractionaldifferentialequations(FDEs)havebeenthefocusofmanystudies due to their frequent appearance in various fields such as physics, chemistry, andengineering[1–4].SeveralmethodshavebeenintroducedtosolveFDE,the popular Laplace transform method [1,2], the iteration method [3], the Fourier transformmethod[5]andtheoperationalmethod[6,7].However,mostofthese methods are suitable for special types of FDEs, mainly the linear with constant coefficients.Recently[8]linearFDEsbasedontheReimann–Liouvilefractional derivative with general variable coefficients are solved by adapting the Applied Mathematics and Computation 131 (2002) 517–529 www.elsevier.com/locate/amc E-mail addresses: shawagnt@ju.edu.jo, shawagnt@index.com.jo (N.T. Shawagfeh). 1 Permanent address: Department of Mathematics, Faculty of Science, University of Jordan, Amman, Jordan. 0096-3003/02/$ - see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII:S0096-3003(01)00167-9