Search

In this study, midpoint-type integral inequalities for $ (s,m) $ (s , m) -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 $ (s,m) $ (s , m) -convex function in the third sense, are also established. This article utilized $ (s,m) $ (s , m) -convex function in the third sense to generalized midpoint-type integral inequalities which give more sharp inequalities. [ABSTRACT FROM AUTHOR]

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.