Fractional Dynamics: Applications of the Caputo Operator in Solving the Sawada–Kotera and Rosenau–Hyman Equations

Khudhayr A. Rashedi, Musawa Yahya Almusawa (), Hassan Almusawa, Tariq S. Alshammari and Adel Almarashi
Additional contact information
Khudhayr A. Rashedi: Deparment of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Musawa Yahya Almusawa: Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia
Hassan Almusawa: Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia
Tariq S. Alshammari: Deparment of Mathematics, College of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Adel Almarashi: Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Saudi Arabia

Mathematics, 2025, vol. 13, issue 2, 1-23

Abstract: This study investigates the fractional-order Sawada–Kotera and Rosenau–Hyman equations, which significantly model non-linear wave phenomena in various scientific fields. We employ two advanced methodologies to obtain analytical solutions: the q-homotopy Mohand transform method (q-HMTM) and the Mohand variational iteration method (MVIM). The fractional derivatives in the equations are expressed using the Caputo operator, which provides a flexible framework for analyzing the dynamics of fractional systems. By leveraging these methods, we derive diverse types of solutions, including hyperbolic, trigonometric, and rational forms, illustrating the effectiveness of the techniques in addressing complex fractional models. Numerical simulations and graphical representations are provided to validate the accuracy and applicability of derived solutions. Special attention is given to the influence of the fractional parameter on behavior of the solution behavior, highlighting its role in controlling diffusion and wave propagation. The findings underscore the potential of q-HMTM and MVIM as robust tools for solving non-linear fractional differential equations. They offer insights into their practical implications in fluid dynamics, wave mechanics, and other applications governed by fractional-order models.

Keywords: Sawada–Kotera equation; Rosenau–Hyman equation; q-homotopy Mohand transform method (q-HMTM); Mohand variational iteration method (MVIM); fractional-order differential equation; Caputo operator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/2/193/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/2/193/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:2:p:193-:d:1562860

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().