A method for solving the generalized Camassa-Choi problem with the Mittag-Leffler function and temporal local derivative

Abstract

This paper focuses on a reduction technique to discover exact solutions for the generalized Camassa-Choi equation with temporal local M-derivative. The paper presents various types of exact solutions along with their corresponding first integrals. Furthermore, the interactions between the orders of α and β in the M-derivative are taken into account and depicted graphically for the derived solutions. Remarkably, the paper demonstrates that in certain situations, exact solutions can be obtained for any value of n, which holds significant mathematical intrigue. The authors note that Nucci's reduction technique has not previously been employed for differential equations with M-derivative, to the best of their knowledge.

Keywords

• Nucci's reduction method
• Local M-derivative
• Generalized Camassa-Choi equation