Hybrid Fractional Estimations for Quadrature Inequalities

Abstract

We study new fractional integral operators that involve linear combinations of Riemann and Caputo fractional integral operators. Thus, under the fundamentals of generalized con vexities, new fractional integral inequalities are explored and investigated for such hybrid fractional integral operators. This enables us to obtain several interfusing cases for frac tional parameter α ≥ 0. In order to derive fractional quadrature-type inequalities, some hybrid quadrature-type integral identities i.e. Simpson’s and Newton’s type in fractional calculus are derived for differentiable functions. Thus, by employing convexities of first and twice differentiable functions, several estimations of quadrature fractional integral in equalities are obtained. Finally, a number of fractional outcomes are provided related to special mean quadrature inequalities, q-digamma functions and Bessel functions