Preprint Article Version 1 This version is not peer-reviewed

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

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. Preprints 2017, 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 a , b , having a continuous derivative g on a , b . For the Lebesgue integrable function f : a , b C , we define the k-g-left-sided fractional integral of f by S k , g , a + f x = a x k g x - g t g t f t d t , x a , b and the k-g-right-sided fractional integral of f by S k , g , b - f x = x b k g t - g x g t f t d t , x [ a , b ) , where the kernel k is defined either on 0 , or on 0 , 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

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