ESTIMATES FOR FRACTIONAL INTEGRALS OF RIEMANN-LIOUVILLE TYPE USING A CLASS OF FUNCTIONS
Authors
Adel Benguessoum
Department of Mathematics, Laboratory of Informatics and Mathematics,
University of Tiaret
Halim Benali
Department of Mathematics, Laboratory of Informatics and Mathematics,
University of Tiaret
Mohammed Said Souid
Department of Economic Sciences, University of Tiaret
Kanokwan Sitthithakerngkiet
Intelligent and Nonlinear Dynamic Innovations Research Center,
Department of Mathematics, Faculty of Applied Science,
King Mongkut's University of Technology North Bangkok
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.