Fractional Ostrowski Type Inequalities via Generalized Mittag–Leffler Function

Abstract

If we study the theory of fractional differential equations then we notice the Mittag–Leffler function is very helpful in this theory. On the contrary, Ostrowski inequality is also very useful in numerical computations and error analysis of numerical quadrature rules. In this paper, Ostrowski inequalities with the help of generalized Mittag–Leffler function are established. In addition, bounds of fractional Hadamard inequalities are given as straightforward consequences of these inequalities.

Inequalities of the Ostrowski Type Associated with Fractional Integral Operators Containing the Mittag–Leffler Function

“…Remark 2. In Theorem 3, for k = 1, we attain Theorem 2 from [22]. For δ = p = 0, we attain Theorem 7 from [23].…”