A comprehensive review of the Hermite-Hadamard inequality pertaining to fractional differential operators

Abstract

A review on Hermite-Hadamard type inequalities connected with a different classes of convexities and fractional differential operators is presented. In the various classes of convexities it includes, classical convex functions, quasi-convex functions, p-convex functions, strongly-m-convex functions, strongly-(θ,m)-convex functions, (s, m)-convex functions, (θ, h- m)-convex functions, strongly (θ, h- m)-convex functions, (h, m)-convex functions of the second type, m-convex functions, h-convex functions, (h,m)-convex functions, relative-convex functions, exponentially (θ, h- m)-convex functions, harmonically h-convex functions and geometric-arithmetically s-convex functions. In the fractional differential operators it includes, Caputo fractional derivative, k-Caputo fractional derivative and Hilfer fractional derivative.

Keywords

• hermite-hadamard inequalities
• convex function
• caputo fractional derivative
• k-caputo fractional derivative
• hilfer fractional derivative