Tempered Fractional Integral Inequalities for Convex Functions

Abstract

Certain new inequalities for convex functions by utilizing the tempered fractional integral are established in this paper. We also established some new results by employing the connections between the tempered fractional integral with the (R-L) fractional integral. Several special cases of the main result are also presented. The obtained results are more in a general form as it reduced certain existing results of Dahmani (2012) and Liu et al. (2009) by employing some particular values of the parameters.

On the weighted fractional integral inequalities for Chebyshev functionals

“…Recently the researchers [29][30][31][32][33][34][35][36][37][38] presented certain remarkable inequalities by considering certain type of fractional integrals. This paper is designed as follows.…”

Certain Weighted Fractional Integral Inequalities for Convex Functions

“…In addition, severel mathematicians have studied certain inequalities for convex functions using different type (for example; R-L fractional integral operator, tempered fractional integral operators, generalized proportional integral operators, generalized proportional Hadamard integral operators) of integral operators. These studies have helped to develop different aspects of operator analysis [9][10][11][12].…”

On Further Inequalities for Convex Functions via Generalized Weighted-Type Fractional Operators

“…In addition, several mathematicians have studied certain inequalities for convex functions using different types of integral operators (for example, the R-L fractional integral operator, the conformable fractional integral operator, tempered fractional integral operators, generalized proportional integral operators, and generalized proportional Hadamard integral operators). These studies have helped to develop different aspects of operator analysis [10][11][12][13][14][15][16]. Different from other mapping classes, convex functions have several applications in the areas of optimization theory, probability theory, statistics, mathematics, and applied sciences.…”