Certain triple q-integral equations involving third Jackson $q$-Bessel functions as kernel

TL;DR

This paper uses fractional q-calculus to solve complex triple q-integral equations with third Jackson q-Bessel functions as kernels, reducing them to simpler Fredholm q-integral equations and providing examples.

Contribution

It introduces a novel approach employing fractional q-calculus to solve triple q-integral equations involving third Jackson q-Bessel functions.

Findings

Solution reduces to two Fredholm q-integral equations of the second kind

Includes explicit examples demonstrating the method

Utilizes existing results to solve dual q^2-integral equations

Abstract

In this paper, we employ the fractional $q$-calculus in solving a triple system of $q$-Integral equations, where the kernel is the third Jackson $q$-Bessel functions. The solution is reduced to two simultaneous Fredholm $q$-integral equation of the second kind. Examples are included. We also apply a result in~[Pacific J. Math. \textbf{275}(1) (2015)63--102] for solutions of dual $q^2$-integral equations to solve certain triple integral equations.