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
Type
journal article in Web of Science
Language
English
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.
Keywords
fractional differential equation; non-commensurate orders; initial value problem; differential transform; fractional power series
Authors
REBENDA, J.
Released
9. 11. 2019
Publisher
MDPI
Location
Basel, Switzerland
ISBN
2073-8994
Periodical
Symmetry
Year of study
11
Number
11
State
Swiss Confederation
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",
journal="Symmetry",
year="2019",
volume="11",
number="11",
pages="1--10",
doi="10.3390/sym11111390",
issn="2073-8994",
url="https://www.mdpi.com/2073-8994/11/11/1390"
}Documents