Publication detail

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

REBENDA, J.

Original Title

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

English Title

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

Type

journal article in Web of Science

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

Released

09.11.2019

Publisher

MDPI

Location

Basel, Switzerland

Pages from

1

Pages to

10

Pages count

10

URL

Full text in the Digital Library

BibTex


@article{BUT159907,
  author="Josef {Rebenda}",
  title="Application of Differential Transform to Multi-Term Fractional Differential Equations with Non-Commensurate Orders",
  annote="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.",
  address="MDPI",
  chapter="159907",
  doi="10.3390/sym11111390",
  howpublished="online",
  institution="MDPI",
  number="11",
  volume="11",
  year="2019",
  month="november",
  pages="1--10",
  publisher="MDPI",
  type="journal article in Web of Science"
}