Modification of optimal homotopy asymptotic method for fractional heat equations

Shakeel Ahmad; Mehreen Fiza; Aasim Ullah Jan; Amjad  Ali; Amjad  Ali; Hakeem Ullah; Syed Muhammad Ghufran

doi:10.5269/bspm.75969

Shakeel Ahmad Abdul Wali Khan University Mardan
Mehreen Fiza Abdul Wali Khan University Mardan
Aasim Ullah Jan Bacha Khan University Charsadda
Amjad Ali Bacha Khan University Charsadda
Amjad Ali Bacha Khan University Charsadda
Hakeem Ullah Abdul Wali Khan University
Syed Muhammad Ghufran Abdul Wali Khan University Mardan

Abstract

In the present paper,Optimal Homotopy Asymptotic Method (OHAM) is used to solve fractional order heat equations.These equation,Which are essential in various scientific and engineering fields,, can present significant challenges due to complexity. Solutions to the fractional-order heat equation in series form are obtained by applying the OHAM. Numerical examples are provided in order to help understand the suggested method’s operation.These examples serve as practical illustrations to help readers grasp how the method operates and the results it can yield. It has been demonstrated using the OHAM that other nonlinear problems may be readily solved with a high rate of convergence and a small volume of calculations. The fractional order is evaluated using the Caputo and Caputo-fabrizio operators. Thus, the OHAM is regarded as one of the best analytical methods for resolving linear and nonlinear equations of fractional order, especially fractional-order heat equations.

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