Truncated Lévy statistics for dispersive transport in disordered semiconductors

Sibatov, Renat T.; Учайкин, В. В.

doi:10.1016/j.cnsns.2011.03.027

Cited by 18 publications

(12 citation statements)

References 25 publications

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“…There are two models of this type in the literature that differ in their mathematical derivations. The corresponding kernels are: [18,19]; and (k5) [19,20].…”

Section: Generalized Fractional Derivativesmentioning

confidence: 99%

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An Inverse Problem for a Generalized Fractional Derivative with an Application in Reconstruction of Time- and Space-Dependent Sources in Fractional Diffusion and Wave Equations

Kinash

Janno

2019

Mathematics

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In this article, we consider two inverse problems with a generalized fractional derivative. The first problem, IP1, is to reconstruct the function u based on its value and the value of its fractional derivative in the neighborhood of the final time. We prove the uniqueness of the solution to this problem. Afterwards, we investigate the IP2, which is to reconstruct a source term in an equation that generalizes fractional diffusion and wave equations, given measurements in a neighborhood of final time. The source to be determined depends on time and all space variables. The uniqueness is proved based on the results for IP1. Finally, we derive the explicit solution formulas to the IP1 and IP2 for some particular cases of the generalized fractional derivative.

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“…There are two models of this type in the literature that differ in their mathematical derivations. The corresponding kernels are: [18,19]; and (k5) [19,20].…”

Section: Generalized Fractional Derivativesmentioning

confidence: 99%

“…where k has one of the above forms (k1)-(k7) [16][17][18]20,23,26,31]. In the latter equation, B = −λ∆ and, in order to guarantee the invertibility of B, proper boundary conditions must be specified in the domain D(B).…”

Section: Formulation Of Inverse Problemsmentioning

confidence: 99%

An Inverse Problem for a Generalized Fractional Derivative with an Application in Reconstruction of Time- and Space-Dependent Sources in Fractional Diffusion and Wave Equations

Kinash

Janno

2019

Mathematics

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“…Introduction of correction in form of some truncations is more or less soft; we obtain an equation with first-order time derivative for long-time asymptotics. These two regions can be combined in a single equation in the case of soft decay by introducing an exponential factor in the kernel of the fractional differential operator [41]:…”

Section: Some Problems and Perspectivesmentioning

confidence: 99%

Nonlocal Models of Cosmic Ray Transport in the Galaxy

Учайкин¹

2015

JAMP

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Studying the cosmic ray transport in the Galaxy, we deal with two interacting substances: charged particles and interstellar magnetic field. Two coupled local equations describe this complicated system, but elimination of one of them (say, the magnetic field equation) transforms remaining one (the cosmic rays equation) into the nonlocal form. The most popular nonlocal operators in the cosmic ray physics are integro-differential operators of fractional order. This report contains review of recent works in this direction, including original results of the author. In the last section, some specific problems are discussed: fractional operators with soft truncation of their kernels, nonlocal properties of fractional Laplacian, and a true form of the fractional material derivative.

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“…The fractional generalizations that are used in this work were motivated by the studies of anomalous diffusion reported in Refs. [19][20][21][22][23][24]. Tateishi et al [19] studied fractional diffusion equation with other forms of fractional time operators instead of the Riemann-Liouville derivative.…”

Section: Introductionmentioning

confidence: 99%

Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators

Sibatov

Sun

2020

Fractal Fract

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The approach based on fractional advection–diffusion equations provides an effective and meaningful tool to describe the dispersive transport of charge carriers in disordered semiconductors. A fractional generalization of Fick’s law containing the Riemann–Liouville fractional derivative is related to the well-known fractional Fokker–Planck equation, and it is consistent with the universal characteristics of dispersive transport observed in the time-of-flight experiment (ToF). In the present paper, we consider the generalized Fick laws containing other forms of fractional time operators with singular and non-singular kernels and find out features of ToF transient currents that can indicate the presence of such fractional dynamics. Solutions of the corresponding fractional Fokker–Planck equations are expressed through solutions of integer-order equation in terms of an integral with the subordinating function. This representation is used to calculate the ToF transient current curves. The physical reasons leading to the considered fractional generalizations are elucidated and discussed.

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Truncated Lévy statistics for dispersive transport in disordered semiconductors

Cited by 18 publications

References 25 publications

An Inverse Problem for a Generalized Fractional Derivative with an Application in Reconstruction of Time- and Space-Dependent Sources in Fractional Diffusion and Wave Equations

An Inverse Problem for a Generalized Fractional Derivative with an Application in Reconstruction of Time- and Space-Dependent Sources in Fractional Diffusion and Wave Equations

Nonlocal Models of Cosmic Ray Transport in the Galaxy

Dispersive Transport Described by the Generalized Fick Law with Different Fractional Operators

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