Abstract
In this paper, we establish two integral identities associated with differentiable functions and the k-Riemann-Liouville fractional integrals. The results are then used to derive the estimates of upper bound for functions whose first or second derivatives absolute values are higher order strongly s-convex functions.
Highlights
Fractional calculus known as noninteger calculus is a branch of mathematical analysis in which we discuss the integrals and derivatives of arbitrary order
UÞy/k−1du, x which implies that Bkðx, yÞ = ð1/kÞBððx/kÞ, ðy/kÞÞ and Bk ðx, yÞ = ΓkðxÞΓkðyÞ/Γkðx + yÞ: Motivated by the ideas of [19, 20], in this paper, we first establish two identities for the k -Riemann-Liouville fractional integrals associated with differentiable functions
We apply the results to derive some estimates of the upper bound for differentiable functions involving k-fractional integrals via higher order strongly s-convex functions
Summary
Fractional calculus known as noninteger calculus is a branch of mathematical analysis in which we discuss the integrals and derivatives of arbitrary order. The study of fractional calculus has a very long history, which can be traced back to the end of the 17th century; in 1695, L’Hospital wrote to Leibniz to discuss fractional derivative about a function. Many mathematicians, such as Euler, Laplace, Fourier, Abel, Liouville, and Riemann, have carried out in-depth research on this subject (see [1]). Due to the backgrounds in practical applications, the fractional calculus has developed rapidly and has become a hot research topic (see [2,3,4]). Among several known forms of fractional integrals, the Riemann-Liouville fractional integral has been investigated extensively, which is defined as follows: Definition 1 ([3]).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
