Modified Modelling for Heat Like Equations within Caputo Operator

Hassan Khan, Adnan Khan, Maysaa Al-Qurashi, Rasool Shah and Dumitru Baleanu
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Hassan Khan: Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan
Adnan Khan: Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan
Maysaa Al-Qurashi: Department of Mathematics, King Saud University, Riyadh 11495, Saudi Arabia
Rasool Shah: Department of Mathematics, Abdul Wali khan University, Mardan 23200, Pakistan
Dumitru Baleanu: Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530 Ankara, Turkey

Energies, 2020, vol. 13, issue 8, 1-14

Abstract: The present paper is related to the analytical solutions of some heat like equations, using a novel approach with Caputo operator. The work is carried out mainly with the use of an effective and straight procedure of the Iterative Laplace transform method. The proposed method provides the series form solution that has the desired rate of convergence towards the exact solution of the problems. It is observed that the suggested method provides closed-form solutions. The reliability of the method is confirmed with the help of some illustrative examples. The graphical representation has been made for both fractional and integer-order solutions. Numerical solutions that are in close contact with the exact solutions to the problems are investigated. Moreover, the sample implementation of the present method supports the importance of the method to solve other fractional-order problems in sciences and engineering.

Keywords: Iterative Laplace Transform method; fractional-order heat equations; Caputo operator; Mittag–Leffler function (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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