We propose a semi-analytical approach based on Taylor’s theorem which is convenient for finding exact or at least approximate solution to the initial value problem for two-term fractional differential equations with Caputo fractional derivatives of noncommensurate orders. We focus on equations with real orders not exceeding 1. The two-term differential equation is first transformed into a two-order system and consequently to a system of recurrence relations which can be solved by computer. Approximation of the solution is given in the form of truncated fractional power series. The choice of order of the fractional power series is discussed and possible values of the order are determined with respect to orders of the equation. An example is included to demonstrate applicability of the approach to the considered problem.
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24 July 2019
INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2018)
13–18 September 2018
Rhodes, Greece
Research Article|
July 24 2019
Application of differential transform to two-term fractional differential equations with noncommensurate orders
Josef Rebenda;
Josef Rebenda
a)
Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology
, Technicka 8, 616 00 Brno, Czech Republic
a)Corresponding author: [email protected]
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Zdeněk Šmarda
Zdeněk Šmarda
b)
Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology
, Technicka 8, 616 00 Brno, Czech Republic
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a)Corresponding author: [email protected]
AIP Conf. Proc. 2116, 310008 (2019)
Citation
Josef Rebenda, Zdeněk Šmarda; Application of differential transform to two-term fractional differential equations with noncommensurate orders. AIP Conf. Proc. 24 July 2019; 2116 (1): 310008. https://doi.org/10.1063/1.5114315
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