New classes of unified fractional integral inequalities

Abstract

<abstract><p>Many researchers in recent years have studied fractional integrals and derivatives. Some authors recently introduced generalized fractional integrals, the so-called unified fractional integrals. In this article, we establish certain new integral inequalities by employing the unified fractional integral operators. In fact, for a class of $ n $ $ (n\in\mathbb{N}), $ positive continuous and decreasing functions on $ [v_1, v_2], $ certain new classes of integral inequalities are discussed. The inequalities established in this manuscript are more general forms of the classical inequalities given in the literature. The existing classical inequalities can be rectified by imposing the conditions stated in remarks. By imposing certain conditions on $ \hbar $ and $ \Lambda $ available in the literature, many new forms of fractional integral inequalities can be produced.</p></abstract>

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

“…Convex analysis has become one of the important application areas of fractional analysis (see [1][2][3][4][5][6][7][8][9]). 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).…”