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Numerical comparison of methods for solving linear differential equations of fractional order. (English) Zbl 1137.65450
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:
65R20 Numerical methods for integral equations
45J05 Integro-ordinary differential equations
26A33 Fractional derivatives and integrals
65L05 Numerical methods for initial value problems
34A30 Linear ordinary differential equations and systems, general
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