On some new inequalities involving generalized Erd\'elyi-Kober fractional $q$-integral operator

TL;DR

This paper establishes new inequalities involving a generalized Erdélyi-Kober fractional q-integral operator with two deformation parameters, extending previous results and highlighting their connections.

Contribution

It introduces novel inequalities for the generalized Erdélyi-Kober fractional q-integral operator with two parameters, expanding the theoretical framework of fractional q-calculus.

Findings

Derived new inequalities for the generalized Erdélyi-Kober fractional q-integral operator.

Connected the new inequalities with existing results in fractional q-calculus.

Extended the theoretical understanding of fractional operators with multiple deformation parameters.

Abstract

In the present investigation, we aim to establish some inequalities involving generalized Erd\'elyi-Kober fractional $q$-integral operator of the two parameters of deformation $q_{1}$ and $q_{2}$ due to Gaulu\'e, by following the same lines used by Baleanu and Agarwal in their recent paper. Relevant connections of the results presented here with those earlier ones are also pointed out.