New fractional integral inequalities for preinvex functions involving Caputo-Fabrizio operator

Abstract

It's undeniably true that fractional calculus has been the focus point for numerous researchers in recent couple of years. The writing of the Caputo-Fabrizio fractional operator has been on many demonstrating and real-life issues. The main objective of our article is to improve integral inequalities of Hermite-Hadamard and Pachpatte type incorporating the concept of preinvexity with the Caputo-Fabrizio fractional integral operator. To further enhance the recently presented notion, we establish a new fractional equality for differentiable preinvex functions. Then employing this as an auxiliary result, some refinements of the Hermite-Hadamard type inequality are presented. Also, some applications to special means of our main findings are presented.

Keywords

• caputo-fabrizio fractional integral
• preinvex functions
• hermite-hadamard inequality
• hölder inequality
• hölder-i̇şcan inequality
• power-mean inequality