A fractional q-integral operator associated with a certain class of q-Bessel functions and q-generating series

Abstract

Abstract This paper deals with Al-Salam fractional q-integral operator and its application to certain q-analogues of Bessel functions and power series. Al-Salam fractional q-integral operator has been applied to various types of q-Bessel functions and some power series of special type. It has been obtained for basic q-generating series, q-exponential and q-trigonometric functions as well. Various results and corollaries are provided as an application to this theory.

Keywords

• Fractional integral
• q-fractional integral operator
• q-analogue
• q-trigonometric function
• q-Bessel function
• q-exponential function