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Zbl 1187.34007
Bataineh, A.S.; Alomari, A.K.; Noorani, M.S.M.; Hashim, I.; Nazar, R.
Series solutions of systems of nonlinear fractional differential equations. (English)
[J] Acta Appl. Math. 105, No. 2, 189-198 (2009). ISSN 0167-8019; ISSN 1572-9036/e

Summary: Differential equations of fractional order (FDE) appear in many applications in physics, chemistry and engineering. An effective and easy-to-use method for solving such equations is needed. In this paper, series solutions of the FDEs are presented using the homotopy analysis method (HAM). The HAM provides a convenient way of controlling the convergence region and rate of the series solution. It is confirmed that the HAM series solutions contain the Adomian decomposition method solution as special cases.

MSC 2000:: *34A08
34A25 Analytical theory of ODE
34A45 Theoretical approximation of solutions of ODE

Keywords: homotopy analysis method; system of nonlinear fractional differential equations; Caputo fractional derivative

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Zentralblatt MATH Berlin [Germany]