The Fractional Integral Inequalities Involving Saigo’s Operator and q-Extension

Document Type : Regular research papers

Authors

1 Mathematics and computing skills, University of Technology and applied sciences, Sultanate of Oman

2 Department of Mathematics, Government College for Women Nawakadal, Srinagar, Jammu and Kashmir, India.

3 Department of Engineering Mathematics and Computing, Madhav Institute of Technology and Science, Gwalior, (M.P.) India.

4 Department of Mathematics, Government Women College Pulwama, Jammu and Kashmir, India.

5 Department of Mathematics and Physics, Government College for Women Nawakadal, Srinagar, Jammu and Kashmir, India.

Abstract

The aim of this present paper is to prove some novel fractional integral inequalities for synchronous functions connected to the Chebyshev functional, involving the Gauss hypergeometric function and presents a number of special instances as fractional integral inequalities involving Riemann-Liouville type fractional integral operators. Additionally, we take into account their applicability to other relevant, previous findings.

Introduction:
The most beneficial uses of fractional integral inequalities are in determining the uniqueness of
solutions to fractional boundary value issues and fractional partial differential equations. Additionally, they offer upper and lower bounds for the solutions of the aforementioned equations.
These factors have prompted a number of scholars working in the area of integral inequalities
to investigate various extensions and generalizations by utilizing fractional calculus operators.
For instance, the book [1] and the publications [2-11] both contain references to such works.
Purohit and Raina [9] recently looked into some integral inequalities of the Chebyshev type
[12] utilizing Saigo fractional integral operators and established the q-extensions of the main
findings. Present study uses the fractional hypergeometric operator proposed by Curiel and
Galue [13] to prove a few generalized integral inequalities for synchronous functions related to
the Chebyshev functional. As special examples of our findings, the results attributed to Purohit
and Raina [9] and Belarbi and Dahmani [2] are presented.

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