A ϱ-Weyl fractional operator of the extended S-type function in a complex domain

This paper proposes a new extension of the well-known S-special function, which is called SM-function. We introduce this function by drawing inspiration from exponential function. This new special function is studied from a variety of analytical perspectives, including differential and integral operators. Furthermore, the ϱ-Weyl fractional integral operator involving the SM-function is studied. These classes are defined by utilizing a new q-differential operator.•The SM- function is provided.•The derivative and integral formulas of the SM-function are studied.•An application of the ϱ-Weyl fractional integral operator associated with the SM-function is investigated. [Display omitted]