Advanced Analysis of Local Fractional Calculus Applied to the Rice Theory in Fractal Fracture Mechanics
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Date
2021
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Abstract
In 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.
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Local Fractional Calculus, Local Fractional Derivative, Local Fractional Integral, Mittag-Leffler Function, Local Fractional Vector Calculus, Local Fractional Partial Differential Equation, Local Fractional Integral Transform, Local Fractional Integral Equation, Local Fractional Inequality, Rice Theory, Fractal Fracture Mechanics, Fractals
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Yang, 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.
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Methods of Mathematical Modelling and Computation for Complex Systems
Volume
373
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Start Page
105
End Page
133