Results 1 to 10 of about 60,664 (263)
Fractional diffusion equation with new fractional operator
Alexandria Engineering Journal, 2020 A new fractional operator with Rabotnov fractional exponential kernel was recently introduced in the literature. In this paper, we consider the fractional diffusion equation in the context of this new fractional operator.
Ndolane Sene
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A fractional diffusion random laser. [PDF]
Sci Rep, 2019 AbstractThe goal of this letter is to introduce the concept of a non-resonant fractional random laser. This is achieved by extending the classical Letokhov model of photon diffusion through disordered gain media to fractional differential operators in space and time.
Chen Y, Fiorentino A, Dal Negro L.
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Analytical solutions and dynamic behavior of conformable fractional reaction-diffusion systems [PDF]
Scientific ReportsThis study presents an analytical investigation of fractional reaction-diffusion systems within the framework of the conformable fractional operator. The conformable operator provides a simplified yet powerful mathematical tool for modeling fractional ...
Azzh Saad Alshehry +2 more
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Fractional diffusion maps [PDF]
Applied and Computational Harmonic Analysis, 2021 In this paper, we extend the diffusion maps algorithm on a family of heat kernels that are either local (having exponential decay) or nonlocal (having polynomial decay), arising in various applications. For example, these kernels have been used as a regularizer in various supervised learning tasks for denoising images.
Antil, Harbir +2 more
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Fractal and Fractional, 2023 The fractional Laplacian operator is a very important fractional operator that is often used to describe several anomalous diffusion phenomena. In this paper, we develop some numerical schemes, including a finite difference scheme and finite volume ...
Junjie Wang, Shoucheng Yuan, Xiao Liu
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Boundary conditions for fractional diffusion [PDF]
Journal of Computational and Applied Mathematics, 2018 This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady state solutions.
Boris Baeumer +3 more
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Fractal-fractional advection–diffusion–reaction equations by Ritz approximation approach
Open Physics, 2023 In this work, we propose the Ritz approximation approach with a satisfier function to solve fractal-fractional advection–diffusion–reaction equations. The approach reduces fractal-fractional advection–diffusion–reaction equations to a system of algebraic
Md Nasrudin Farah Suraya +2 more
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Fractional chemotaxis diffusion equations [PDF]
Physical Review E, 2010 We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding.
Langlands, T. A. M., Henry, B. I.
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Similarity Solutions to Nonlinear Diffusion/Harry Dym Fractional Equations
Advances in Mathematical Physics, 2021 By using scalar similarity transformation, nonlinear model of time-fractional diffusion/Harry Dym equation is transformed to corresponding ordinary fractional differential equations, from which a travelling-wave similarity solution of time-fractional ...
Chao Yue +3 more
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Numerical methods for fractional diffusion [PDF]
Computing and Visualization in Science, 2018 We present three schemes for the numerical approximation of fractional diffusion, which build on different definitions of such a non-local process. The first method is a PDE approach that applies to the spectral definition and exploits the extension to one higher dimension.
Andrea Bonito +4 more
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