ESTIMATES FOR FRACTIONAL INTEGRALS OF RIEMANN-LIOUVILLE TYPE USING A CLASS OF FUNCTIONS

Abstract

In this paper, our research focuses on fractional integral inequalities involving h-convex functions. These inequalities, which extend classical integral inequalities to fractional orders and incorporate the concept of h-convexity. In this direction, we present a weighted fractional integral operator which generalizes than of Riemann-Liouville, characterized by two parameters, and two non-negative weight functions. This study leads to establish some fractional integral inequalities via a special class of functions called h-convex. As consequence, some estimates and bounds for Laplace transform of some functions are obtained, also bounds for left hand side and right of Riemann-Liouville integrals, which lead to the well-known Hermite-Hadamard inequality.