Montgomery Identity and Ostrowski Type Inequalities for Riemann-Liouville Fractional Integral

Abstract

We present Montgomery identity for Riemann-Liouville fractional integral as well as for fractional integral of a functionfwith respect to another functiong. We further use them to obtain Ostrowski type inequalities involving functions whose first derivatives belong toLpspaces. These inequalities are generally sharp in casep>1and the best possible in casep=1. Application for Hadamard fractional integrals is given.

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

“…For several Ostrowski type inequalities for Riemann-Liouville fractional integrals see [6]- [21], [22]- [32] and the references therein.…”

Ostrowski Type Inequalities Involving ψ-Hilfer Fractional Integrals

“…Studies involving integral inequalities are important in several areas such as mathematics, physics, chemistry, biology, engineering and others [6][7][8][9][10][11][12][13][14][15]. We recall that there are many definitions of fractional operators, including Riemann-Liouville (RL), Hadamard, Liouville, Weyl (see [16][17][18][19]). From such fractional integrals, one can obtain generalizations of the inequalities: Hadamard, Hermite-Hadamard, Hardy, Opial, Gruss, and Montgomery, among others [20][21][22][23][24][25][26][27][28][29][30][31][32].…”

“…In recent years, such inequalities have been generalized and developed by many researchers. Various authors obtained new Ostrowski-type inequalities for different fractional operators, see [16][17][18][19][35][36][37][38][39][40][41][42][43][44][45][46][47] and the references therein.…”

“…In 2013, Yue [38] obtained Ostrowski inequalities for both fractional integrals and associated fractional integrals. In 2014, Aljinević [16] studied Montgomery identities for fractional integrals of a function f with respect to another function g. Also, he gave the Ostrowski inequality for fractional integrals for functions whose first derivatives belong to L p spaces. In the same year, Yıldırım and Kırtay [46] established new generalizations for Ostrowski inequalities by using the generalized RL fractional integral.…”

Ostrowski and Trapezoid Type Inequalities for the Generalized <em>k</em>-<em>g</em>-Fractional Integrals of Functions with Bounded Variation

“…For several Ostrowski type inequalities for Riemann-Liouville fractional integrals see [2]- [17], [19]- [32] and the references therein.…”