Baleanu, D.Srivastava, H.M.Yang, X.-J.2024-02-152025-09-182024-02-152025-09-182022Yang, 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. 105-133.2198-4182https://doi.org/10.1007/978-3-030-77169-0_5https://hdl.handle.net/20.500.12416/14432In 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. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.eninfo:eu-repo/semantics/closedAccessFractal Fracture MechanicsFractalsLocal Fractional CalculusLocal Fractional DerivativeLocal Fractional InequalityLocal Fractional IntegralLocal Fractional Integral EquationLocal Fractional Integral TransformLocal Fractional Partial Differential EquationLocal Fractional Vector CalculusMittag-Leffler FunctionRice TheoryBook Part10.1007/978-3-030-77169-0_52-s2.0-85114901266