Fractional Integral Inequalities concerning Extended Bessel Function in the Kernel

Arshad Hussain,Jihad Younis,Muhammad Iqbal,Muhammad Samraiz,Gauhar Rahman,Xiaolong Qin

doi:10.1155/2021/7325102

Abstract

The major purpose of this paper is to use the fractional integral operator in terms of extended generalized Bessel function to estimate new fractional integral inequalities for the extended Chebyshev functional in the sense of synchronous functions. We prove a set of inequalities for the fractional integral operator in terms of extended generalized Bessel function integrals with one and two parameters. Also, we discussed some special cases of the obtained result.

Highlights

Integral inequalities are essential in the subject of fractional differential equations
As a result of these novel fractional integral operators, future research will focus on developing new ideas for connecting fractional operators by addressing new fractional integral inequalities. e interested readers are referred to [22,23,24]
We present fractional integral inequalities for the extended Chebyshev functional in the sense of synchronous functions by utilizing integral operator (8)

Summary

Introduction

Integral inequalities are essential in the subject of fractional differential equations. In [6], certain inequalities for the generalized (k, ρ)-fractional integral operator were proposed. E generalized Hermite–Hadamard-type inequalities via fractional integral operators were proposed in [7]. By using a family of n positive functions, Dahmani [8] developed several fractional integral inequalities. In [16,17,18,19,20,21], some numerous developments of fractional integral operators and their applications in various domains can be found. Kashuri and Liko [25] and Luo et al [26] presented certain remarkable integral inequalities for the generalized fractional integrals. Tilahun et al [32] proposed an extended form of the fractional integral containing Bessel function in the kernel by ρ. We present fractional integral inequalities for the extended Chebyshev functional in the sense of synchronous functions by utilizing integral operator (8)

Main Results

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Concluding Remarks