Fractional q-Calculus Operators Pertaining to the q-Analogue of M-Function and Its Application to Fractional q-Kinetic Equations

In this article, the authors introduce the q-analogue of the M-function, and establish four theorems related to the Riemann–Liouville fractional q-calculus operators pertaining to the newly defined q-analogue of M-functions. In addition, to establish the solution of fractional q-kinetic equations involving the q-analogue of the M-function, we apply the technique of the q-Laplace transform and the q-Sumudu transform and its inverse to obtain the solution in closed form. Due to the general nature of the q-calculus operators and defined functions, a variety of results involving special functions can only be obtained by setting the parameters appropriately.