Baleanu, DumitruYang, Xiao-JunBaleanu, DumitruSrivastava, H. M.2024-02-152024-02-152021Yang, Xiao-Jun; Baleanu, Dumitru; Srivastava, H. M. (2021). "Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics", in Methods of Mathematical Modelling and Computation for Complex Systems, Vol. 373, pp. 105-133.https://hdl.handle.net/20.500.12416/7244In this chapter, the recent results for the analysis of local fractional calculus are considered for the first time. The local fractional derivative (LFD) and the local fractional integral (LFI) in the fractional (real and complex) sets, the series and transforms involving the Mittag-Leffler function defined on Cantor sets are introduced and reviewed. The uniqueness of the solutions of the local fractional differential and integral equations and the local fractional inequalities are considered in detail. The local fractional vector calculus is applied to describe the Rice theory in fractal fracture mechanics.eninfo:eu-repo/semantics/closedAccessLocal Fractional CalculusLocal Fractional DerivativeLocal Fractional IntegralMittag-Leffler FunctionLocal Fractional Vector CalculusLocal Fractional Partial Differential EquationLocal Fractional Integral TransformLocal Fractional Integral EquationLocal Fractional InequalityRice TheoryFractal Fracture MechanicsFractalsBook Part373105133