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

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.


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
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