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Zbl 1119.65127
Momani, Shaher; Odibat, Zaid
Numerical approach to differential equations of fractional order. (English)
[J] J. Comput. Appl. Math. 207, No. 1, 96-110 (2007). ISSN 0377-0427

Summary: The variational iteration method and the Adomian decomposition method are implemented to give approximate solutions for systems of linear and nonlinear 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 differential equations. In these schemes, the solution takes the form of a convergent series with easily computable components. This paper presents a numerical comparison between the two methods for solving systems of fractional differential equations. Numerical results show that the two approaches are easy to implement and accurate when applied to differential equations of fractional order.

MSC 2000:: *65R20 Integral equations (numerical methods)
45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations
65L05 Initial value problems for ODE (numerical methods)
34A34 Nonlinear ODE and systems, general
26A33 Fractional derivatives and integrals (real functions)

Keywords: variational iteration method; Lagrange multiplier; Adomian decomposition method; fractional differential equations; caputo fractional derivative; numerical comparison; numerical results

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Zentralblatt MATH Berlin [Germany]