Derivation of Bounds of an Integral Operator via Exponentially Convex Functions

Abstract EN

In this paper, bounds of fractional and conformable integral operators are established in a compact form.

By using exponentially convex functions, certain bounds of these operators are derived and further used to prove their boundedness and continuity.

A modulus inequality is established for a differentiable function whose derivative in absolute value is exponentially convex.

Upper and lower bounds of these operators are obtained in the form of a Hadamard inequality.

Some particular cases of main results are also studied.