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

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Authors :

Rahmatullah Ibrahim Nuruddeen 1 *, F. D. Zaman 2 and Yusuf F. Zakariya 3

Author Address :

1 Department of Mathematics, Federal University Dutse, Jigawa State, Nigeria.
2 Abdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.
3 Department of Mathematics, Department of Science Education, Ahmadu Bello University, Zaria, Nigeria.

*Corresponding author.

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.

DOI :

10.26637/MJM0702/0012

Article Info :

Received : November 29, 2018; Accepted : January 09, 2019.

 

 

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