Analytic solutions of fractional kinetic equations involving incomplete ℵ-function

This paper expressed the fractional kinetic equation (KE) in terms of the incomplete Formula: see text-function, I-function, Fox H-function, and Meijer’s G-function. It assesses the importance of fractional KE in diverse scientific and engineering contexts, highlighting its relevance across various scenarios. In this paper, we investigate the results of Katugampola’s kinetic fractional equations with the product of the generalized M-series and incomplete Formula: see text-function. The Formula: see text-Laplace transform is applied for obtaining the desired results. Utilizing an M-series, the universality of this series is harnessed to deduce solutions for a fractional KE. Furthermore, a graphical representation of the obtained solutions’ behaviors is presented, enhancing the impact of the findings.