Fractional-order partial differential equations describing propagation of shallow water waves depending on power and Mittag-Leffler memory

AIMS Mathematics

article

Maysaa Al Qurashi¹  Saima Rashid²  Sobia Sultana³  Fahd Jarad⁴  Abdullah M. Alsharif⁷ 

[1] Department of Mathematics, King Saud University;Department of Mathematics, Government College University, Faisalabad;Department of Mathematics, Imam Mohammad Ibn Saud Islamic University;Department of Mathematics, Cankaya University;Department of Medical Research, China Medical University Hospital, China Medical University;Department of Mathematics, King Abdulaziz University;Department of Mathematics and Statistics, College of Science, Taif University

关键词: Whitham–Broer–Kaup equation;    Aboodh transform;    $ \bar{\mathbf{q}} $-homotopy analysis transform method;    Atangana-Baleanu fractional derivative;    convergence analysis;   

DOI  :  10.3934/math.2022697

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

In this research, the $ \bar{\mathbf{q}} $-homotopy analysis transform method ($ \bar{\mathbf{q}} $-HATM) is employed to identify fractional-order Whitham–Broer–Kaup equation (WBKE) solutions. The WBKE is extensively employed to examine tsunami waves. With the aid of Caputo and Atangana-Baleanu fractional derivative operators, to obtain the analytical findings of WBKE, the predicted algorithm employs a combination of $ \bar{\mathbf{q}} $-HAM and the Aboodh transform. The fractional operators are applied in this work to show how important they are in generalizing the frameworks connected with kernels of singularity and non-singularity. To demonstrate the applicability of the suggested methodology, various relevant problems are solved. Graphical and tabular results are used to display and assess the findings of the suggested approach. In addition, the findings of our recommended approach were analyzed in relation to existing methods. The projected approach has fewer processing requirements and a better accuracy rate. Ultimately, the obtained results reveal that the improved strategy is both trustworthy and meticulous when it comes to assessing the influence of nonlinear systems of both integer and fractional order.

【 授权许可】

CC BY