Local Fractional Integral Transforms and Their Applications

By Xiao-jun Yang, Dumitru Băleanu, Hari M. Srivastava. 2015

364 citations recorded by the source corpus.

Subfields: Applied Mathematics, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/1ef8203236c61e8979e60612e280ec074c99fc2e

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In Applied Mathematics

In Modeling and Simulation

Citations in the corpus

Fractional derivatives of constant and variable orders applied to anomalous relaxation models in heat-transfer problems (2016, methodology): “Fractional derivatives (FDs) were utilized to model the complex phenomenon in science and engineering practice [1,2,3,4,5,6,7].”
A NEW FRACTIONAL DERIVATIVE WITHOUT SINGULAR KERNEL Application to the Modelling of the Steady Heat Flow (2015, methodology): “More recently, the fractional Caputo-Fabrizio derivative operator without singular kernel was given [1, 9-12]:”
Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel (2016, background): “For the first nonlocal fractional derivatives with nonsingular exponential kernel we refer to [12, 13, 19, 25] and the references therein and for other local approaches of the fractional derivatives we refer to the”
Fractional-Order Derivatives and Integrals: Introductory Overview and Recent Developments (2020, background): “Several important definitions have been introduced for fractional-order derivatives, including: the Riemann-Liouville, the Grünwald-Letnikov, the Liouville-Caputo, the Caputo-Fabrizio and the Atangana-Baleanu fractional-order derivatives (see, for example, [7, 12, 14, 31, 64, 112]).”
An analysis for heat equations arises in diffusion process using new Yang‐Abdel‐Aty‐Cattani fractional operator (2020, neutral): “Similarly, we get Dμt ( D((2)) t Υ(η, t) ) = D((2)) t (YACDμt Υ(η, t)) .”
Non-Differentiable Exact Solutions for the Nonlinear ODEs Defined on Fractal Sets (2017, neutral): “Φτ (μ) = φ3 [φ1 − φ2Tτ (ρμτ )] 2 κ , (43)”
A new fractional operator of variable order: Application in the description of anomalous diffusion (2016, methodology): “POD using the function kernel of the exponential type were reported in [12,13,14,15].”
On the generalized fractional derivatives and their Caputo modification (2017, background): “On the other hand, many researchers work on fractional integrals and derivatives with non-local and non-singular kernels [7, 9, 17, 22, 23].”
Solution of fractional-order differential equations based on the operational matrices of new fractional Bernstein functions (2017, background): “Yang et al. (2015) presented local fractional derivative operators and local integral transforms to solve fractional differential equations.”
On novel nondifferentiable exact solutions to local fractional Gardner's equation using an effective technique (2020, background): “4 APPLICATION OF THE METHOD First of all, incorporating the concept of local differential definition (4) in Gardner's equation (1), the following structure for the equations is obtained: ∂Ξν(μ, η) ∂ην + ρ2Ξν(μ, η) ∂Ξν(μ, η) ∂μν + ρ3Ξ(2)ν(μ, η) ∂Ξν(μ, η) ∂μν + ρ4 ∂Ξν(μ, η) ∂μ4ν = 0.”