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Fractional order partial differential equations, as generalization of classical integer order partial differential equations, are increasingly used to model problems in fluid flow, finance and other areas of applications. In this paper we present a collection of numerical algorithms for the solution of nonlinear partial differential equations with space- and time-fractional derivatives. The fractional derivatives are considered in the Caputo sense. Two numerical examples are given to demonstrate the effectiveness of the present methods. Results show that the numerical schemes are very effective and convenient for solving nonlinear partial differential equations of fractional order.

In this paper, variational iteration and homotopy perturbation methods that developed for integer-order differential equations are directly extended to derive explicit and numerical solutions of various evolution equations with time-fractional derivatives. The results reveal that the two methods are very effective and convenient for solving nonlinear partial differential equations of fractional order.

Momani, Shaher M./0000-0002-6326-8456; Odibat, Zaid/0000-0002-2414-7969 WOS: 000294083500016 In this paper, a fractional order differential system for modeling human T-cell lymphotropic virus I (HTLV-I) infection of CD4(+) T-cells is studied and its approximate solution is presented using a multi-step generalized differential transform method. The method is only a simple modification of the generalized differential transform method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding systems. The solutions obtained are also presented graphically. (C) 2011 Elsevier Ltd. All rights reserved.