Abstract:

In the paper, the authors use local fractional calculus theory and the definition of generalized convex function on the α type set of the real line numbers \begin{document}$\mathbb{R}$\end{document}^α, some new Simpson-type inequalities involving local fractional integrals are established. Finally, some applications of our obtained inequalities to special means and numerical integration are given.

Key words: Simpson-type inequalities, Generalized convex function, Local fractional derivative, Local fractional integral