Version 1
: Received: 6 December 2017 / Approved: 6 December 2017 / Online: 6 December 2017 (08:32:00 CET)
How to cite:
Dragomir, S.S. Ostrowski and Trapezoid Type Inequalities for the Generalized k-g-Fractional Integrals of Functions with Bounded Variation. Preprints2017, 2017120034 (doi: 10.20944/preprints201712.0034.v1).
Dragomir, S.S. Ostrowski and Trapezoid Type Inequalities for the Generalized k-g-Fractional Integrals of Functions with Bounded Variation. Preprints 2017, 2017120034 (doi: 10.20944/preprints201712.0034.v1).
Cite as:
Dragomir, S.S. Ostrowski and Trapezoid Type Inequalities for the Generalized k-g-Fractional Integrals of Functions with Bounded Variation. Preprints2017, 2017120034 (doi: 10.20944/preprints201712.0034.v1).
Dragomir, S.S. Ostrowski and Trapezoid Type Inequalities for the Generalized k-g-Fractional Integrals of Functions with Bounded Variation. Preprints 2017, 2017120034 (doi: 10.20944/preprints201712.0034.v1).
Abstract
Let g be a strictly increasing function on having a continuous derivative g′ on For the Lebesgue integrable function , we define the k-g-left-sided fractional integral of f by and the k-g-right-sided fractional integral of f by where the kernel k is defined either on or on with complex values and integrable on any finite subinterval. 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.
Subject Areas
generalized Riemann-Liouville fractional integrals; Hadamard fractional integrals; functions of bounded variation; Ostrowski type inequalities; Trapezoid inequalities
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.