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

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

WoS Article

The differential transformation, an approach based on Taylor’s theorem, is proposed as convenient for finding an 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 gives a reliable and expected outcome including the phenomenon of symmetry in choice of orders of the differential transformation of the multi-order system.

The differential transformation, an approach based on Taylor’s theorem, is proposed as convenient for finding an 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 gives a reliable and expected outcome including the phenomenon of symmetry in choice of orders of the differential transformation of the multi-order system.

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

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

REBENDA, J.

2020

09.11.2019

MDPI

Basel, Switzerland

2073-8994

Symmetry-Basel

11

11

Swiss Confederation

1

10

10

https://www.mdpi.com/2073-8994/11/11/1390

http://hdl.handle.net/11012/180783

symmetry-11-01390