Application of the q-Homotopy Analysis Transform Method to Fractional-Order Kolmogorov and Rosenau–Hyman Models within the Atangana–Baleanu Operator

Author:

Yasmin Humaira1ORCID,Alshehry Azzh Saad2,Saeed Abdulkafi Mohammed3ORCID,Shah Rasool4,Nonlaopon Kamsing5ORCID

Affiliation:

1. Department of Basic Sciences, Preparatory Year Deanship, King Faisal University, Al-Ahsa 31982, Saudi Arabia

2. Department of Mathematical Sciences, Faculty of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

3. Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia

4. Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan

5. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Abstract

The q-homotopy analysis transform method (q-HATM) is a powerful tool for solving differential equations. In this study, we apply the q-HATM to compute the numerical solution of the fractional-order Kolmogorov and Rosenau–Hyman models. Fractional-order models are widely used in physics, engineering, and other fields. However, their numerical solutions are difficult to obtain due to the non-linearity and non-locality of the equations. The q-HATM overcomes these challenges by transforming the equations into a series of linear equations that can be solved numerically. The results show that the q-HATM is an effective and accurate method for solving fractional-order models, and it can be used to study a wide range of phenomena in various fields.

Funder

Princess Nourah bint Abdulrahman University

King Faisal University

Publisher

MDPI AG

Subject

Physics and Astronomy (miscellaneous),General Mathematics,Chemistry (miscellaneous),Computer Science (miscellaneous)

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