Application of the generalized q-Mittag-Leffler function to fractional q-kinetic equations via q-Shehu transform - Mulugeta Dawud Ali; D.L. Suthar (Kuwait Journal of Science)
This paper investigates the properties and applications of q-Mittag-Leffler functions with five parameters within the framework of fractional q-kinetic equations. We study the essential properties of these functions using several q-calculus operators, including the q-Riemann-Liouville integral, generalized q-Weyl derivative operators, and q-transform such as the q-Mellin and q-Shehu transforms. An original method for addressing fractional q-kinetic equations involving generalized q-Mittag-Leffler functions is presented, which utilizes the q-Shehu transform, a generalization of the q-Laplace transform. Further, we state some significant and special cases of our main results. Finally, we present the obtained solutions in the form of numerical graphs using MATLAB 23 software.