A Novel Approach to Solving Fractional-Order Kolmogorov and Rosenau–Hyman Models through the q-Homotopy Analysis Transform Method

Laila F. Seddek, Essam R. El-Zahar, Jae Dong Chung and Nehad Ali Shah ()
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Laila F. Seddek: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi Arabia
Essam R. El-Zahar: Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam bin Abdulaziz University, P.O. Box 83, Al-Kharj 11942, Saudi Arabia
Jae Dong Chung: Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea
Nehad Ali Shah: Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea

Mathematics, 2023, vol. 11, issue 6, 1-11

Abstract: In this study, a novel method called the q-homotopy analysis transform method (q-HATM) is proposed for solving fractional-order Kolmogorov and Rosenau–Hyman models numerically. The proposed method is shown to have fast convergence and is demonstrated using test examples. The validity of the proposed method is confirmed through graphical representation of the obtained results, which also highlights the ability of the method to modify the solution’s convergence zone. The q-HATM is an efficient scheme for solving nonlinear physical models with a series solution in a considerable admissible domain. The results indicate that the proposed approach is simple, effective, and applicable to a wide range of physical models.

Keywords: Laplace transform; fractional-order Kolmogorov; Rosenau–Hyman equations; Atangana-Baleanu-Caputo derivative; q-homotopy analysis transform method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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