Generalizations of Hermite–Hadamard like inequalities involving $\chi _{{\kappa }}$-Hilfer fractional integrals

Author:

Chu Yu-Ming,Awan Muhammad UzairORCID,Talib Sadia,Noor Muhammad Aslam,Noor Khalida Inayat

Abstract

AbstractThe main objective of this paper is to obtain a new κ-fractional analogue of Hermite–Hadamard’s inequality using the class of s-convex functions and $\chi _{{\kappa }}$ χ κ -Hilfer fractional integrals. In order to obtain other main results of the paper we derive two new fractional integral identities using the definitions of $\chi _{{\kappa }}$ χ κ -Hilfer fractional integrals. For the validity of these identities we also take some particular examples. Using these identities we then obtain some more new variants of Hermite–Hadamard’s inequality using s-convex functions.

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Algebra and Number Theory,Analysis

Reference20 articles.

1. Awan, M.U., Talib, S., Chu, Y.M., Noor, M.A., Noor, K.I.: Some new refinements of Hermite–Hadamard-type inequalities involving $\psi _{k}$-Riemann–Liouville fractional integrals and applications. Math. Probl. Eng. 2020, Article ID 3051920 (2020)

2. Breckner, W.W.: Stetigkeitsaussagen fiir eine Klasse verallgemeinerter convexer funktionen in topologischen linearen Raumen. Publ. Inst. Math. 23, 13–20 (1978)

3. Dragomir, S.S., Pearce, C.E.M.: Selected topics on Hermite–Hadamard inequalities and applications, Victoria University, Australia (2000)

4. Ghaffar, A., Ali, A., Ahmed, S., Akram, S., Junjua, M-.U-.D., Baleanu, D., Nisar, K.S.: A novel analytical technique to obtain the solitary solutions for nonlinear evolution equation of fractional order. Adv. Differ. Equ. 2020, 308 (2020)

5. Hilfer, R. (ed.): Applications of Fractional Calculus in Physics World Scientific, Singapore (2000)

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