Preprint Article Version 1 This version is not peer-reviewed

Application of Differential Transform to Multi-Term Fractional Differential Equations with Non-Commensurate Orders

Version 1 : Received: 30 September 2019 / Approved: 2 October 2019 / Online: 2 October 2019 (05:55:33 CEST)

A peer-reviewed article of this Preprint also exists.

Rebenda, J. Application of Differential Transform to Multi-Term Fractional Differential Equations with Non-Commensurate Orders. Symmetry 2019, 11, 1390. Rebenda, J. Application of Differential Transform to Multi-Term Fractional Differential Equations with Non-Commensurate Orders. Symmetry 2019, 11, 1390.

Journal reference: Symmetry 2019, 11, 1390
DOI: 10.3390/sym11111390

Abstract

The differential transformation, an approach based on Taylor's theorem, is proposed as convenient for finding exact or approximate solution to the initial value problem with multiple Caputo fractional derivatives of generally non-commensurate orders. The multi-term differential equation is first transformed into a multi-order system and then into a system of recurrence relations for coefficients of formal fractional power series. The order of the fractional power series is discussed in relation to orders of derivatives appearing in the original equation. Application of the algorithm to an initial value problem results in a reliable and expected outcome.

Subject Areas

fractional differential equation; non-commensurate orders; initial value problem; differential transform; fractional power series

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