Estimates of Classes of Generalized Special Functions and Their Application in the Fractional k , s -Calculus Theory

Abstract

In this article, we aim to develop new $\left(k,s\right)$ -fractional integral and differential operators containing $S$ -functions as kernels in a form of generalized $k$ -Mittag-Leffer functions. We also set up various properties of such operators. Furthermore, we consider a variety of implications of the major outcomes that will be very useful in the implementation of scientific, engineering, and technical problems.