COMPREHENSIVE ANALYSIS OF INNOVATIVE FRACTAL-FRACTIONAL DIFFERENTIAL OPERATORS UTILIZING THE GENERALIZED MITTAG-LEFFLER FUNCTION FOR KINETIC SYSTEMS: APPLICATION TO THE LANGMUIR–HINSHELWOOD REACTION MODEL

Abstract

The primary objective of this study is to develop novel difference operators by incorporating the generalized Mittag-Leffler function with fractal derivatives within the framework of kinetic equations. The operators referred to as the Fractal-Fractional Differential Operator and Fractal–Fractional Integral Operator are used to apply to new mathematical fractional models. The primary role is to deal with non-local phenomena in the world and this shows fractal as well as dynamical characteristics. This study investigates the novel properties of these operators, numerical approximation methods for the computation of these operators and their applications in solving different practical problems in real life. The purpose of the research is to improve approaches to bring methods to bear on complex systems with fractal and fractional characteristics. The accuracy of the operators in solving the differential equation systems that were obtained from the kinetic models is shown in the graphical and numerical results and they are found to be excellent.