New Estimates of Integral Inequalities via Generalized Proportional Fractional Integral Operator With Respect to Another Function

Abstract

In this paper, the newly proposed concept of the generalized proportional fractional integral operator with respect to another function [Formula: see text] has been utilized to generate integral inequalities using convex function. This new concept will have the option to reduce self-similitudes in the fractional attractors under investigation. We discuss the implications and other consequences of the integral inequalities concerning the generalized proportional fractional integral operator with respect to another function [Formula: see text] are derived here and these outcomes permit us specifically to generalize some classical inequalities. Certain intriguing subsequent consequences of the fundamental hypotheses are also figured. It is to be supposed that this investigation will provide new directions in the quantum theory of capricious nature.

Certain Matrix Riemann–Liouville Fractional Integrals Associated with Functions Involving Generalized Bessel Matrix Polynomials

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“…Therefore many authors proposed different numerical techniques to find Simpson-type inequalities, arising in the substantial literature of numerical analysis and engineering, and many other fields of sci-ences [1][2][3][4][5][6][7][8][9][10][11][12]. Profusely novel versions of Simpson-type inequalities for the class of convex functions have been modified and generalized by numerous researchers [13][14][15][16][17][18][19][20][21][22][23][24]. Recently, many investigations about (1.1) can be found by Rashid et al [25] for preinvex functions, Li and Du [26] for (α, m)-GA-convex functions, Xi and Qi [27] for logarithmically convex functions, Sarikaya et al [28] for s-convex functions and İşcan et al [29] for p-convex function.…”

Some Trapezium-Like Inequalities Involving Functions Having Strongly n-Polynomial Preinvexity Property of Higher Order

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