Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals

Abstract

An analogous version of Chebyshev inequality, associated with the weighted function, has been established using the pathway fractional integral operators. The result is a generalization of the Chebyshev inequality in fractional integral operators. We deduce the left sided Riemann Liouville version and the Laplace version of the same identity. Our main deduction will provide noted results for an appropriate change to the Pathway fractional integral parameter and the degree of the fractional operator.

Improvement in Some Inequalities via Jensen–Mercer Inequality and Fractional Extended Riemann–Liouville Integrals

“…Mathematical analysts are increasingly drawn to a technique known as "fractional operators" analysis. Integral inequalities with fractional integrals are very important because they may be used to check the solution advantages for many different types of integrodifferential fractional or fractal equations [11][12][13].…”

On the weighted fractional integral inequalities for Chebyshev functionals

“…We refer the reader to [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. The existence and uniqueness of a miscible flow equation through porous media with a nonsingular fractional derivative, unified integral inequalities comprising pathway operators, certain results comprising the weighted Chebyshev functional using pathway fractional integrals and integral inequalities associated with Gauss hypergeometric function fractional integral operator can be found in [22][23][24][25]. Elezovic et al [26] proved the following inequality for WCF:…”

Pathway Fractional Integral Operator on Some τ-extensions of Lauricella Functions of Several Variables

“…Many authors have contributed works on the Pathway fractional integral operator, which is associated with a variety of special functions including the Aleph function and generalized polynomials [20,34], the H-function, the M-series [8,9,24], the Mittag-Leffler type function [27], the generalized k-Mittag-Leffler function [30], the new generalized Mittag-Leffler function [33], the Struve function [29], the composition of two functions [3,15], the Mainardi function [5], the product of two Aleph functions [6], the Gimel function [1], the composition of Hurwitz-Lerch zeta function [21], the weighted Chebyshev function [26], the incomplete H-functions [4] and the modified multivariable H-function [16].…”