Midpoint-type integral inequalities for (s, m)-convex functions in the third sense involving Caputo fractional derivatives and Caputo–Fabrizio integrals

Abstract

In this study, midpoint-type integral inequalities for [Formula: see text]-convex function in the third sense, involving Caputo fractional derivatives and Caputo–Fabrizio integral operators, are demonstrated. Inequalities, containing Caputo–Fabrizio integral operators for functions, whose derivatives are [Formula: see text]-convex function in the third sense, are also established. This article utilized [Formula: see text]-convex function in the third sense to generalized midpoint-type integral inequalities which give more sharp inequalities.

Keywords

• Convex function
• integral inequalities
• Caputo fractional derivatives
• Caputo–Fabrizio integral operators
• 39B62
• 39B05