Ostrowski and Trapezoid Type Inequalities for the Generalized $k$-$g$-Fractional Integrals of Functions with Bounded Variation

Abstract

In this paper we establish some Ostrowski and trapezoid type inequalities for the k-g-fractional integrals of functions of bounded variation. Applications for mid-point and trapezoid inequalities are provided as well. Some examples for a general exponential fractional integral are also given.

On parameterized inequalities of Ostrowski and Simpson type for convex functions via generalized fractional integrals

“…In addition to this, many researchers focused on establishing Ostrowski type inequalities for certain fractional integral operators, such as k-Riemann-Liouville fractional integrals, local fractional integrals, and Raina fractional integrals. For more information and unexplained subjects, we refer the reader to previous studies [7][8][9][10][11][12][13] and the references therein.…”

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

“…In [41], Set first obtained the Riemann-Liouville fractional version of the Ostrowski inequality for s-convex functions. In addition to this, many researchers focused on establishing Ostrowski type inequalities for certain fractional integral operators, such as k-Riemann-Liouville fractional integrals [16], local fractional integrals [34], Raina fractional integrals [2], generalized k-g-fractional integrals [10] and ψ-Hilfer fractional integrals [5]. On the other hand, several Ostrowski inequalities for coordinated convex mapping in involving double Riemann integrals and double Riemann-Liouville fractional integrals are introduced in [24] and [23], respectively.…”

On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables

“…Furthermore, many studies were focused on the proof of Ostrowski-type inequalities for certain fractional integral operators, such as k-Riemann-Liouville fractional integrals [8], local fractional integrals [9], Raina fractional integrals [10], etc. (see [11][12][13][14][15][16][17][18][19][20][21][22][23]). Moreover, by utilizing co-ordinated convex mapping, several Ostrowski inequalities were presented for the Riemann integral and Riemann-Liouville fractional integrals in [24,25], respectively.…”