THERMAL SCIENCE

International Scientific Journal

Imran Talib

,

Md. Nur Alam

,

Dumitru Baleanu

,

Danish Zaidi

A DECOMPOSITION ALGORITHM COUPLED WITH OPERATIONAL MATRICES APPROACH WITH APPLICATIONS TO FRACTIONAL DIFFERENTIAL EQUATIONS

ABSTRACT
In this article, we solve numerically the linear and non-linear fractional initial value problems of multiple orders by developing a numerical method that is based on the decomposition algorithm coupled with the operational matrices approach. By means of this, the fractional initial value problems of multiple orders are decomposed into a system of fractional initial value problems which are then solved by using the operational matrices approach. The efficiency and advantage of the developed numerical method are highlighted by comparing the results obtained otherwise in the literature. The construction of the new derivative operational matrix of fractional legendre function vectors in the Caputo sense is also a part of this research. As applications, we solve several fractional initial value problems of multiple orders. The numerical results are displayed in tables and plots.
KEYWORDS
fractional legendre function vectors, Caputo derivative, multi order fractional differential equations, spectral tau method, spectral collocation method
PAPER SUBMITTED: 2021-07-28
PAPER REVISED: 2021-08-08
PAPER ACCEPTED: 2021-08-12
PUBLISHED ONLINE: 2021-12-18
DOI REFERENCE: https://doi.org/10.2298/TSCI21S2449T
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Special issue 2, PAGES [449 - 455]
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A decomposition algorithm coupled with operational matrices approach with applications to fractional differential equations

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence