Construction of Generalized k-Bessel–Maitland Function with Its Certain Properties

Abstract

The main motive of this study is to present a new class of a generalized $k$ -Bessel–Maitland function by utilizing the $k$ -gamma function and Pochhammer $k$ -symbol. By this approach, we deduce a few analytical properties as usual differentiations and integral transforms (likewise, Laplace transform, Whittaker transform, beta transform, and so forth) for our presented $k$ -Bessel–Maitland function. Also, the $k$ -fractional integration and $k$ -fractional differentiation of abovementioned $k$ -Bessel–Maitland functions are also pointed out systematically.