Trapezoid type inequalities for generalized Riemann-Liouville fractional integrals of functions with bounded variation

Abstract

In this paper we establish some trapezoid type inequalities for the Riemann-Liouville fractional integrals of functions of bounded variation and of Hölder continuous functions. Applications for the g-mean of two numbers are provided as well. Some particular cases for Hadamard fractional integrals are also provided.

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.…”

Some generalized fractional trapezoid and Ostrowski type inequalities for functions with bounded partial derivatives

“…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 works 9–29 and the references therein. 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 Latif et al 30 and Latif and Hussain, 31 respectively.…”

Further inequalities for the generalized k-g-fractional integrals of functions with bounded variation

“…For several Ostrowski type inequalities for Riemann-Liouville fractional integrals see [2]- [17], [21]- [34] and the references therein.…”