Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics

Discrete Local Fractional Hilbert-type Inequalities

“…Over the last ten years, by using the kinds of generalized fractional integral operators, a great deal of fractional integral inequalities have been presented [2][3][4][5]. Recently, local fractional calculus has caused widespread attention from many scholars, we give basic definitions and results of the local fractional calculus (see [6][7][8][9][10][11][12][13]). Based on the local fractal identity and the generalized p-convexity, some novel Newton's type variants for the local differentiable functions were obtained in the paper [14].…”

“…For the sake of convenience, we recall Yang's fractal set Ω α , where the set Ω is called base set of fractional set, and α denotes the dimension of cantor set, 0 < α ≤ 1. The α-type set of integers Z α is defined by (see [6][7][8])…”