A note on fractional Simpson-like type inequalities for functions whose third derivatives are convex

Abstract

In this paper, equality is established for Riemann-Liouville fractional integral. With the aid of this equality, it is proved some fractional Simpson-like type inequalities for functions whose third derivatives in absolute value are convex. By using special cases of the main results, previously obtained Simpson type inequalities are found for the Riemann-Liouville fractional integral. Furthermore, the mathematical example is presented to verify the newly established inequality.