Relaxation and Diffusion Models With Non-Singular Kernels
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Date
2017
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier Science Bv
Open Access Color
HYBRID
Green Open Access
No
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Publicly Funded
No
Abstract
Anomalous relaxation and diffusion processes have been widely quantified by fractional derivative models, where the definition of the fractional-order derivative remains a historical debate due to its limitation in describing different kinds of non-exponential decays (e.g. stretched exponential decay). Meanwhile, many efforts by mathematicians and engineers have been made to overcome the singularity of power function kernel in its definition. This study first explores physical properties, of relaxation and diffusion models where the temporal derivative was defined recently using an exponential kernel. Analytical analysis shows that the Caputo type derivative model with an exponential kernel cannot characterize non-exponential dynamics well-documented in anomalous relaxation and diffusion. A legitimate extension of the previous derivative is then proposed by replacing the exponential kernel with a stretched" exponential kernel. Numerical tests show that the Caputo type derivative model with the stretched exponential kernel can describe a much wider range of anomalous diffusion than the exponential kernel, implying the potential applicability of the new derivative in quantifying real-world, anomalous relaxation and diffusion processes. (C) 2016 Elsevier B.V. All rights reserved.
Description
Keywords
Anomalous Relaxation And Diffusion, Non-Singular Kernel, Stretched Exponential Function Kernel, Memory Characterization, Mean Squared Displacement, stretched exponential function kernel, Classical dynamic and nonequilibrium statistical mechanics (general), non-singular kernel, memory characterization, mean squared displacement, Fractional partial differential equations, anomalous relaxation and diffusion
Turkish CoHE Thesis Center URL
Fields of Science
0103 physical sciences, 01 natural sciences
Citation
Baleanu, D..., [et.al.]. (2017). Relaxation and diffusion models with non-singular kernels. Physica A Statistical Mechanics And Its Applications, 468, 590-596. http://dx.doi.org/ 10.1016/j.physa.2016.10.066
WoS Q
Q2
Scopus Q
Q1

OpenCitations Citation Count
54
Source
Physica A: Statistical Mechanics and its Applications
Volume
468
Issue
Start Page
590
End Page
596
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Scopus : 63
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