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.
