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Zbl 1133.65116
Odibat, Zaid; Momani, Shaher
Numerical methods for nonlinear partial differential equations of fractional order. (English)
[J] Appl. Math. Modelling 32, No. 1, 28-39 (2008). ISSN 0307-904X

Summary: We implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving nonlinear partial differential equations of fractional order. The fractional derivatives are described in the Caputo sense. The two methods in applied mathematics can be used as alternative methods for obtaining analytic and approximate solutions for different types of fractional differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. Numerical results show that the two approaches are easy to implement and accurate when applied to partial differential equations of fractional order.

MSC 2000:: *65R20 Integral equations (numerical methods)
45K05 Integro-partial differential equations
65M70 Spectral, collocation and related methods (IVP of PDE)
35K55 Nonlinear parabolic equations
26A33 Fractional derivatives and integrals (real functions)

Keywords: variational iteration method; Adomian decomposition method; Lagrange multiplier; fractional differential equation; Caputo fractional derivative; numerical results

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Zentralblatt MATH Berlin [Germany]