Abstract
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.