On Some Inequalities Involving Liouville-Caputo Fractional Derivatives and Applications to Special Means of Real Numbers

We are concerned with the class of functions f 2 C1 ([a, b]; R), a, b 2 R, a < b, such that j cD a a f j is convex or fifi cD a b f fifi is convex, where 0 < a < 1, cD a a f is the left-side Liouville-Caputo fractional derivative of order a of f and cD a b f is the right-side Liouville-Caputo fractional derivative of order a of f. Some extensions of Dragomir-Agarwal inequality to this class of functions are obtained. A parallel development is made for the class of functions f 2 C1 ([a, b]; R) such that j cD a a f j is concave or fifi cD a b f fifi is concave. Next, an application to special means of real numbers is provided.