Fractional comparative analysis of Camassa-Holm and Degasperis-Procesi equations

This paper focuses on novel approaches to finding solitary wave (SW) solutions for the modified Degasperis-Procesi and fractionally modified Camassa-Holm equations. The study presents two innovative methodologies: the Yang transformation decomposition technique and the homotopy perturbation transformation method. These methods use the Caputo sense fractional order derivative, the Yang transformation, the adomian decomposition technique, and the homotopy perturbation method. The inquiry effectively solves the fractional Camassa-Holm and Degasperis-Procesi equations, which also provides a detailed numerical and graphical comparison of the solutions found. The results, which include accurate solutions, derived solutions, and absolute error displayed in tabular style, demonstrate the effectiveness of the suggested procedures. These procedures are iterative, which results in several answers. The estimated absolute error attests to the correctness and simplicity of these solutions. Especially in plasma physics, these approaches may be expanded to handle various linear and nonlinear physical issues, including the evolution equations controlling nonlinear waves.