Yuping Yu, Xiaoman Yuan, Taigui Qin, Tingsong Du, Error bounds on the Hermite-Hadamard- and Bullen-type inequalities for $2\alpha$-local fractional derivative, Vol. 2023 (2023), Article ID 34, pp. 1-29

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DOI: 10.23952/jnfa.2023.34

Received April 23, 2023; Accepted October 7, 2023; Published October 30, 2023

Abstract. We present a general integral identity involving $2\alpha$ -local fractional derivative. Based on the integral identity and the fact that the $2\alpha$ -local fractional derivative in absolute value is generalized (s,P)-convex, we establish certain integral inequalities that cover each case of the generalized Hermite-Hadamard’s and Bullen type for the class of mappings. Certain applications in $\alpha$ -type special means, probability distribution mappings, the trapezoidal and midpoint formulas, and wave equations on Cantor sets are presented to demonstrate the validity of the obtained results as well.

How to Cite this Article:
Y. Yu, X. Yuan, T. Qin, T. Du, Error bounds on the Hermite-Hadamard- and Bullen-type inequalities for $2\alpha$-local fractional derivative, J. Nonlinear Funct. Anal. 2023 (2023) 34.