Local Fractional Integral Transforms

By Xiao-jun Yang. 2011

134 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/742b8334c518162cdff84b2c6bf19080be490f35

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Citations in the corpus

Systems of Navier-Stokes equations on Cantor sets (2013, unknown): “Based on it, the Schrödinger equation [28], the heat conduction equation [27, 29], the wave equation [27, 30], and the diffusion equation on Cantor time-space [31] were suggested based on local fractional calculus theory [27, 32, 33].”
Advanced Local Fractional Calculus and Its Applications (2012, unknown): “[11] X.”
On the local fractional wave equation in fractal strings (2019, unknown): “∑ ∞ n1⁄40 pvn ξ; η ð Þ 1⁄4 η β Γ 1þ β ð Þβ ξ β þ pL β 1 z2β Lβ ∂ ∑ ∞ n1⁄40 pvn ξ; η ð Þ ∂ξ 2 664 3 775 2 664 3 775: (25)”
Application of the Fractional Complex Transform to Fractional Differential Equations (2011, unknown): “Many useful transforms for solving various problems were appeared in open literature, such as the travelling wave transform [1], the Laplace transform [2], the Fourier transform [3], the Bäcklund transformation [4], the integral transform [5], and the local fractional integral transforms[6].”
Fractal heat conduction problem solved by local fractional variation iteration method (2013, background): “The local fractional integral of T(x) of order a in the interval [a, b] is defined by [5-7, 22-24]:”
Local fractional series expansion method for solving wave and diffusion equations on Cantor sets (2013, unknown): “In contrast, the local fractional calculus is one of the best candidates for dealing with such problems [26–44].”
A Local Fractional Integral Inequality on Fractal Space Analogous to Anderson’s Inequality (2014, methodology): “Some of the concepts of the local fractional derivative were established in [3–26].”
Generalizations of Hölder’s and Some Related Integral Inequalities on Fractal Space (2011, unknown): “As a consequence, the theory of local fractional calculus becomes important for modelling problems for fractal mathematics and engineering on Cantor sets and it plays important role in many applications in several fields such as the theoretical physics [14, 18], the elasticity and fracture mechanics”