THERMAL SCIENCE

International Scientific Journal

A NEW APPROACH TO FRACTIONAL DIFFERENTIAL EQUATIONS

ABSTRACT
In this work, we define fractional derivative of order ς > 0, with no restrictions on the domain of the function, and give its geometry. We derive some rules and properties for the proposed new approach and show that if fractional order converges to an integer order, then each rule converges to the corresponding rule of derivative under this integer. On applications side we show that it has ability to convert various type of FDE to ODE and vice versa. Finally, we solve several FDE given in literature through the new approach.
KEYWORDS
PAPER SUBMITTED: 2022-06-11
PAPER REVISED: 2022-06-24
PAPER ACCEPTED: 2022-07-04
PUBLISHED ONLINE: 2023-04-08
DOI REFERENCE: https://doi.org/10.2298/TSCI23S1301A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special issue 1, PAGES [301 - 309]
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© 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