Certain inequalities via generalized proportional Hadamard fractional integral operators

Abstract

In the article, we introduce the generalized proportional Hadamard fractional integrals and establish several inequalities for convex functions in the framework of the defined class of fractional integrals. The given results are generalizations of some known results.

Certain Hadamard Proportional Fractional Integral Inequalities

“…Recently Jarad et al [46] introduced the idea of generalized proportional fractional integral operators which comprises exponential in their kernels. Later on, Rahman et al [47] studied these operators and defined Hadamard proportional fractional integrals. They established certain inequalities for convex functions by employing Hadamard proportional fractional integrals.…”

“…Houas [45] utilized Hadamard fractional integrals and established several weighted type integral inequalities. Recently, Jarad et al [46] and Rahman et al [47] proposed the idea of non-local fractional proportional and Hadamard proportional integrals which concerning exponential functions in their kernels. The aim of this paper is to establish weighted type inequalities by using the non-local Hdamard proportional integrals.…”

Bounds of Generalized Proportional Fractional Integrals in General Form via Convex Functions and Their Applications

“…In [44], Rahman et al discussed some specific new types of integral inequalities for a class of n (n ∈ N) positive continuous and decreasing functions on [r, b]. Rahman et al [45] defined the generalized proportional Hadamard fractional integrals and established certain new integral inequalities for convex functions. In [46][47][48][49][50], certain remarkable inequalities, properties, and applications can be found.…”

Tempered Fractional Integral Inequalities for Convex Functions

“…Dahmani [47] presented some classes of fractional integral inequalities by considering a family of n positive functions. Certainly, remarkable inequalities such as Hermite-Hadamard type [48], Chebyshev type [49][50][51], inequalities via generalized conformable integrals [52], Grüss type [53,54], fractional proportional inequalities and inequalities for convex functions [55], Hadamard proportional fractional integrals [56], bounds of proportional integrals with applications [57], inequalities for the weighted and the extended Chebyshev functionals [58], certain new inequalities for a class of n(n ∈ N) positive continuous and decreasing functions [59] and certain generalized fractional inequalities [60] are recently presented by utilizing several different kinds of fractional calculus approaches.…”