On inequalities of Simpson's type for convex functions via generalized fractional integrals

Abstract

Fractional calculus and applications have application areas in many different fields such as physics, chemistry, and engineering as well as mathematics. The application of arithmetic carried out in classical analysis in fractional analysis is very important in terms of obtaining more realistic results in the solution of many problems. In this study, we prove an identity involving generalized fractional integrals by using differentiable functions. By utilizing this identity, we obtain several Simpson’s type inequalities for the functions whose derivatives in absolute value are convex. Finally, we present some new results as the special cases of our main results.