Certain Results Associated with q-Fractional Integrals and Some Application

Fractional differential equations have recently received a great attention by various researchers due to their excellence and effective role in different fields of science including physics, control theory, engineering, signal processing and fractional dynamics as well. In this paper we aim to discuss Al-Salam fractional q-integral operator on certain q-analogues of Bessel functions. We give definitions and derive results and formulas utilizing a series form of certain fractional integral. Further, apply the generalized new fractional integral to q-Bessel functions of types, one, two and three as well. Multiplication of more two q-Bessel functions of same order is also considered to generalize the singular case.