(k,s)-Riemann-Liouville fractional integral and applications

Abstract

In this paper, we introduce a new approach on fractional integration, which generalizes the Riemann-Liouville fractional integral. We prove some properties for this new approach. We also establish some new integral inequalities using this new fractional integration.

$${\varvec{(k,s)}}$$ ( k , s ) -Riemann–Liouville fractional integral inequalities for continuous random variables

“…In a recent paper [20], Sarikaya et al have introduced a new fractional integration which generalizes both the k-Riemann-Liouville and Katugampola's fractional integrals into a single form as the following.…”

Generalized hypergeometric k-functions via (k,s)-fractional calculus

“…Very recently, Sarikaya et al [19] have introduced the (k; s)-Riemann-Liouville fractional integral of order µ > 0 defined by…”

Random variable inequalities involving (k,s)-integration

“…In a very recent work, M. Tomar et al [17] proposed new integral inequalities for the (k, s)−fractional expectation and variance functions of a continuous random variable. Motivated by the results presented in [3,4,6,14,17], in this paper, we present some random variable integral inequalities for the (k, s)−fractional operator.…”