Generalizations of Hermite–Hadamard like inequalities involving $\chi _{{\kappa }}$-Hilfer fractional integrals
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Abstract The 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.
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2021 ◽
Vol 4
(2)
◽
pp. 12-28