On Caputo fractional derivative inequalities by using strongly $ (\alpha, h-m) $-convexity

• Published in: AIMS mathematics Vol. 7; no. 6; pp. 10165 - 10179
• Main Authors: Yan, Tao, Farid, Ghulam, Bibi, Sidra, Nonlaopon, Kamsing
• Format: Journal Article
• Language: English
• Published: AIMS Press 01.01.2022
• Subjects: caputo fractional derivative; convex function; hadamard inequality; h−m)-convex function; strongly (α; strongly convex function
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2022565

In the literature of mathematical inequalities, one can have different variants of the well-known Hadamard inequality for CFD (Caputo fractional derivatives). These variants include generalizations, extensions and refinements which have been proved by defining new classes of functions. This paper aims to formulate inequalities of the Hadamard type which will simultaneously produce refinements and generalizations of many fractional versions of such inequalities that already exist in the literature. The error bounds of some existing inequalities are also proved by applying well-known identities. The results given in this paper are improvements of several well-known Hadamard type Caputo fractional derivative inequalities.