On some inequalities for generalized s-convex functions and applications on fractal sets

Abstract

The authors present some new inequalities of generalized Hermite-Hadamard's type for the class of functions whose second local fractional derivatives of order α in absolute value at certain powers are generalized s-convex functions in the second sense. Moreover, some applications are given. c 2017 all rights reserved.

A non-differentiable solution for the local fractional telegraph equation

“…Local fractional calculus [1] has played an important role in the field of mathematical science and mathematical physics, such as the generalized convex [2] and s-convex [3,4] functions on fractal sets, and Pompeiu-type [5], Steffensen [6], Hermite-Hadamard [7], Holder [8], Hilbert [9], Korteweg-de Vries [10], Burgers [11], Boussinesq [12], heat conduction [13], diffusion [14,15], tricomi [16], Goursat [17], and others [18][19][20][21].…”