Certain results associated with q-Agarwal fractional integral operators and a q-class of special functions

Abstract

This article investigates certain q-analogue of the fractional Agarwal integral operator and its application to a class of polynomials and a series of functions. By utilizing various types of q-Bessel functions, the fractional q-Agarwal integral has been discussed and formulated in a series expression form involving q-shifted factorials and gamma functions. Moreover, certain results and applications of the q-Bessel theory are reported by establishing suitable forms of the fractional integral. Furthermore, the fractional Agarwal integral has been evaluated for some multiple power series formulas. Meanwhile, some desirable results involving q-generating Heine’s series of the first type are provided. Over and above, certain conclusions associated with various exponential, hyperbolic sine and cosine functions are analysed.

Keywords

• Agarwal fractional operator
• q-Jackson
• fractional q-integral
• q-Bessel functions
• q-generating Heines series
• Primary 54C40, 14E20