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

• DOI: 10.3390/math13020193
• Publication Date: 2025-01-08T16:56:22Z
• Authors: Khudhayr A. Rashedi; Musawa Yahya Almu...; Hassan Almusawa; Tariq S. Alshammari; Adel Almarashi
• Keywords: Operator (biology); Dynamics

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: q-homotopy Mohand transform method (q-HMTM) variational iteration (MVIM). The fractional derivatives equations are expressed using Caputo operator, provides a flexible framework for analyzing dynamics of systems. By leveraging these methods, we derive diverse types solutions, including hyperbolic, trigonometric, rational forms, illustrating effectiveness techniques addressing complex models. Numerical simulations graphical representations provided validate accuracy applicability derived solutions. Special attention is given influence parameter on behavior solution behavior, highlighting its role controlling diffusion propagation. findings underscore potential q-HMTM MVIM as robust tools solving differential equations. They offer insights into their practical implications fluid dynamics, mechanics, other applications governed by