Analysing the fractional heat diffusion equation solution in comparison with the new fractional derivative by decomposition method

Rahmatullah Ibrahim Nuruddeen; F. D. Zaman; Yusuf F. Zakariya

doi:10.26637/MJM0702/0012

Abstract

With the current raised issues on the new conformable fractional derivative having satisfied the Leibniz rule for derivatives which was proved not to be so for a differential operator to be fractional among others; we in the present article consider the fractional heat diffusion models featuring fractional order derivatives in both the Caputo’s and the new conformable derivatives to further investigate this development by analyzing two solutions. A comparative analysis of the temperature distributions obtained in both cases will be established. The Laplace transform in conjunction with the well-known decomposition method by Adomian is employed. Finally, some
graphical representations and tables for comparisons are provided together with comprehensive remarks.

Keywords:

Caputo derivative, Conformable derivative, Heat diffusion models, Decomposition method, Laplace transform

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Rahmatullah Ibrahim Nuruddeen Department of Mathematics, Federal University Dutse, Jigawa State, Nigeria.
F. D. Zaman Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
Yusuf F. Zakariya Department of Mathematics, Department of Science Education, Ahmadu Bello University, Zaria, Nigeria. https://orcid.org/0000-0002-5266-8227

Pages: 213-222
Date Published: 01-04-2019
Vol. 7 No. 02 (2019): Malaya Journal of Matematik (MJM)

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