Fractional Ostrowski-type Inequalities via (α, β, γ, δ)−convex Function

bstract. In this paper, we are introducing for the first time a generalized class named the class of (α, β, γ, δ)−convex functions of mixed kind. This generalized class contains many subclasses includ-ing the class of (α, β)−convex functions of the first and second kind,(s, r)−convex functions of mixed kind, s−convex functions of the first and second kind, P−convex functions, quasi-convex functions and the class of ordinary convex functions. In addition, we would like to state the generalization of the classical Ostrowski inequal-ity via fractional integrals, which is obtained for functions whose first derivative in absolute values is (α, β, γ, δ)− convex function of mixed kind. Moreover, we establish some Ostrowski-type inequali-ties via fractional integrals and their particular cases for the class of functions whose absolute values at certain powers of derivatives are (α, β, γ, δ)− convex functions of mixed kind using different tech-niques including Hölder’s inequality and power mean inequality. Also, various established results would be captured as special cases. Moreover, the applications of special means will also be discussed.