Next Article in Journal
Investigations of Laser Produced Plasmas Generated by Laser Ablation on Geomaterials. Experimental and Theoretical Aspects
Previous Article in Journal
Exponentiation in QED and Quasi-Stable Charged Particles
Previous Article in Special Issue
Periodic Solution of a Non-Smooth Double Pendulum with Unilateral Rigid Constrain
Open AccessArticle

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

CEITEC BUT, Brno University of Technology, Purkynova 123, 612 00 Brno, Czech Republic
Symmetry 2019, 11(11), 1390; https://doi.org/10.3390/sym11111390
Received: 30 September 2019 / Revised: 31 October 2019 / Accepted: 6 November 2019 / Published: 9 November 2019
(This article belongs to the Special Issue Nonlinear Oscillations and Boundary Value Problems)
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 fractional differential equation; non-commensurate orders; initial value problem; differential transform; fractional power series
MDPI and ACS Style

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

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop