Generalized differential transform method: Application to differential equations of fractional order. (English) Zbl 1141.65092

Odibat, Zaid; Momani, Shaher; Erturk, Vedat Suat

Appl. Math. Comput. 197, No. 2, 467-477 (2008).

The authors first give some generalizations of the classical version of Taylor’s theorem. These generalizations involve fractional differential operators in the sense of Caputo. Based on these results they then extend the well known Taylor expansion method for the solution of first-order differential equations to the case of differential equations of fractional order. As a result, one obtains a series expansion of the solution that converges under suitable conditions. A truncation of the expansion yields an approximate solution.

Reviewer: Kai Diethelm (Braunschweig)

MSC:

65R20	Numerical methods for integral equations
26A33	Fractional derivatives and integrals
34K05	General theory of functional-differential equations
34K07	Theoretical approximation of solutions to functional-differential equations
45J05	Integro-ordinary differential equations
65L05	Numerical methods for initial value problems involving ordinary differential equations
65L20	Stability and convergence of numerical methods for ordinary differential equations

Keywords:

fractional derivative; Caputo derivative; Taylor’s theorem; differential transform method; convergence; Taylor expansion method; differential equations of fractional order; series expansion

References:

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