THERMAL SCIENCE

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Sertan Alkan

APPROXIMATE ANALYTICAL SOLUTIONS OF A CLASS OF NON-LINEAR FRACTIONAL BOUNDARY VALUE PROBLEMS WITH CONFORMABLE DERIVATIVE

ABSTRACT
In this paper, it is presented that an approximate solution of a class of non-linear differential equations with conformable derivative under boundary conditions by using sinc-Galerkin method that is not used to approximately solve the class of the considered equation in the literature. In the method, the solution function is expressed as a finite series in terms of composite translated sinc functions and the unknown coefficients. The problem is reduced into a non-linear matrix-vector system via sinc grid points, and when this system is solved by using Newton’s method, the unknown coefficients of the solution function are easily obtained. Also, error analysis and some test problems are presented to illustrate the applicability and accuracy of the proposed method.
KEYWORDS
Nonlinearity, sinc-Galerkin method, fractional boundary value problems, conformable derivative
PAPER SUBMITTED: 2020-05-04
PAPER REVISED: 2020-10-21
PAPER ACCEPTED: 2020-10-27
PUBLISHED ONLINE: 2021-01-24
DOI REFERENCE: https://doi.org/10.2298/TSCI200504013A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2021, VOLUME 25, ISSUE Special issue 1, PAGES [121 - 130]
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Approximate analytical solutions of a class of non-linear fractional boundary value problems with conformable derivative

© 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