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Zbl 1137.65450
Momani, Shaher; Odibat, Zaid
Numerical comparison of methods for solving linear differential equations of fractional order. (English)
[J] Chaos Solitons Fractals 31, No. 5, 1248-1255 (2007). ISSN 0960-0779

Summary: We implement relatively new analytical techniques, the variational iteration method and the Adomian decomposition method, for solving linear differential equations of fractional order. 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. This paper will present a numerical comparison between the two methods and a conventional method such as the fractional difference method for solving linear differential equations of fractional order. The numerical results demonstrate that the new methods are quite accurate and readily implemented.

MSC 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations
26A33 Fractional derivatives and integrals (real functions)
65L05 Initial value problems for ODE (numerical methods)
34A30 Linear ODE and systems

Keywords: variational iteration method; Adomian decomposition method; linear differential equations of fractional order; numerical comparison; numerical results

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Zentralblatt MATH Berlin [Germany]