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The Fractional Investigation of Fornberg-Whitham Equation Using an Efficient Technique

Hassan Khan1,2, Poom Kumam3,4,*, Asif Nawaz1, Qasim Khan1, Shahbaz Khan1
1 Department of Mathematics, Abdul Wali Khan University, Mardan, 23200, Pakistan
2 Department of Mathematics, Near East University TRNC, Mersin, 10, Turkey
3 Center of Excellence in Theoretical and Computational Science (TaCS-CoE) & KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Departments of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand
4 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan
* Corresponding Author: Poom Kumam. Email:
(This article belongs to this Special Issue: Fractal-Fractional Models for Engineering & Sciences)

Computer Modeling in Engineering & Sciences 2023, 135(1), 259-273.

Received 09 January 2022; Accepted 17 May 2022; Issue published 29 September 2022


In the last few decades, it has become increasingly clear that fractional calculus always plays a very significant role in various branches of applied sciences. For this reason, fractional partial differential equations (FPDEs) are of more importance to model the different physical processes in nature more accurately. Therefore, the analytical or numerical solutions to these problems are taken into serious consideration and several techniques or algorithms have been developed for their solution. In the current work, the idea of fractional calculus has been used, and fractional Fornberg Whitham equation (FFWE) is represented in its fractional view analysis. A well-known method which is residual power series method (RPSM), is then implemented to solve FFWE. The RPSM results are discussed through graphs and tables which conform to the higher accuracy of the proposed technique. The solutions at different fractional orders are obtained and shown to be convergent toward an integer-order solution. Because the RPSM procedure is simple and straightforward, it can be extended to solve other FPDEs and their systems.


Caputo derivative; fractional partial differential equations; fornberg-whitham; residual power series method

Cite This Article

Khan, H., Kumam, P., Nawaz, A., Khan, Q., Khan, S. (2023). The Fractional Investigation of Fornberg-Whitham Equation Using an Efficient Technique. CMES-Computer Modeling in Engineering & Sciences, 135(1), 259–273.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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