Generalized fractional order kinetic equations involving multi-index Mittag-Leffler functions of several variables

Fractional kinetic equations play a crucial role in a variety of fields, such as in chemical engineering, environmental science, chemistry, signal processing, biology, and medicine. Fractional kinetic equations provide powerful tools for understanding and modeling complex systems in chemistry and chemical engineering and are also very useful in determining the particle reaction rate. Motivated by the important applications of fractional kinetic equations, we address certain generalized fractional differential equations that involve a multivariable generalized multi-index Mittag-Leffler function. Applying the Laplace transform, we derive solutions to these fractional differential equations expressed in terms of the generalized Lauricella function and Prabhakar's Mittag-Leffler function. Our findings are general and encompass several previously established results.