Local Fractional Functional Analysis and Its Applications

By Xiaojun Yang. 2011

259 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/469e24cd72068e9ddc6970d823d3d6f9c668f257

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Citations in the corpus

The Yang-Laplace Transform for Solving the IVPs with Local Fractional Derivative (2014, methodology): “Recently, owing to limit of classical and fractional differential equations, the local fractional differential equations have been applied to describe nondifferentiable problems for the heat and wave in fractal media [22, 23], the structure relation in fractal elasticity [24], and Fokker-Planck equa”
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 Laplace Variational Iteration Method for Solving Diffusion and Wave Equations on Cantor Sets within Local Fractional Operators (2015, methodology): “2 Mathematical Problems in Engineering The local fractional Laplace operator is given by [28, 29] as follows: ∇ 2α = ∂ 2α”
Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015, result): “We have taken the present occasion, as a compliment to our previous survey [107], to cite books published during the years 2011 [92, 80, 44, 26, 65, 47, 5, 106, 117], 2012 [7, 3, 77, 1, 51, 38, 102, 56, 122, 15, 112, 110, 118], 2013 [14, 18, 89, 29, 36], and 2014 [57, 4, 121, 39, 105, 40, 66, 86, 2,”
Generalizations of Hölder’s and Some Related Integral Inequalities on Fractal Space (2011, background): “1 .[15] Let f(x), g(x) ≥ 0, p > 1, 1 p + 1 q = 1 , then 1 Γ(1 + α) ∫ b a |f(x)g(x)| (dx) ≤ ( 1 Γ(1 + α) ∫ b a |f(x)| (dx) )1/p ( 1 Γ(1 + α) ∫ b a |g(x)| (dx) )1/q , (2.”
The Chronicles of Fractional Calculus (2017, unknown): “2009 [6, 90, 122, 27, 89, 77, 155] [109, 17] 2010 [111, 31, 133, 165, 46] [98, 106, 63] 2011 [156, 144, 87, 65, 126, 92, 3, 187, 207, 78, 44, 93] [86, 18]”