Self-similar characteristics of neural networks based on Fokker–Planck equation

Kamitani, Yoshinobu; Matsuba, Ikuo

doi:10.1016/s0960-0779(03)00388-6

Cited by 11 publications

(7 citation statements)

References 11 publications

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“…The FPE is aspired in reaction-kinetics [8]. Some other technical aspects of these equations have been studied by He and Wu [9], Jumarie [10], Kamitani and Matsuba [11], Xu et al [12], and Zak [13].…”

Section: Introductionmentioning

confidence: 99%

Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method

et al. 2019

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In this article, Optimal Homotopy Asymptotic Method (OHAM) is used to approximate results of time-fractional order Fokker-Planck equations. In this work, 3rd order results obtained through OHAM are compared with the exact solutions. It was observed that results from OHAM have better convergence rate for time-fractional order Fokker-Planck equations. The solutions are plotted and the relative errors are tabulated.

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Section: Introductionmentioning

confidence: 99%

Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method

et al. 2019

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“…where > 0, > 0, 0 < ≤ 1, and is the Caputo fractional derivative defined by (7) and initial condition is V ( , 0) = .…”

Section: Example 1 Consider the Nonlinear Time Fractional Fpementioning

confidence: 99%

“…The FPE arises in kinetic theory [4] where it describes the evolution of the one-particle distribution function of a dilute gas with long-range collisions, such as a Coulomb gas. Some applications of this type of equations can be worked out in the works of He and Wu [5], Jumarie [6], Kamitani and Matsuba [7], Xu et al [8], and Zak [9].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of Space-Time Fractional Fokker-Planck Equation by Homotopy Perturbation Sumudu Transform Method

Dubey

Alkahtani

Atangana

2015

Mathematical Problems in Engineering

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An efficient approach based on homotopy perturbation method by using Sumudu transform is proposed to solve some linear and nonlinear space-time fractional Fokker-Planck equations (FPEs) in closed form. The space and time fractional derivatives are considered in Caputo sense. The homotopy perturbation Sumudu transform method (HPSTM) is a combined form of Sumudu transform, homotopy perturbation method, and He’s polynomials. The nonlinear terms can be easily handled by the use of He’s polynomials. Some examples show that the HPSTM is an effective tool for solving many space time fractional partial differential equations.

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“…FPE is emerging in various areas of natural science, along with quantum mechanics, circuit theory, chemical physics, solid state physics and theoretical biology. For a little utilization of FPE, reference can be made to works by Xu et al [27] , Jumarie [10], He and Wu [9], Kamitani and Matsuba [11], and Zak [31]. The motion of the concentration field w(ξ ,t) of the single space variable x at the time t for the general FPE shall be given by [22] ∂ w ∂t = − ∂ ∂ ξ A(ξ ) + ∂ 2 ∂ ξ 2 B(ξ ) w(ξ ,t) (1.1)…”

Section: Introductionmentioning

confidence: 99%

An efficient analytical approach for solving fractional Fokker-Planck equations

Bairwa¹,

Singh²

2020

Malaya J. Mat

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The present study focuses on investigating the approximate analytical solutions of linear and non-linear Fokker-Planck equations (FPEs) with space-and time-fractional derivatives using an efficient analytical method, namely the Sumudu transform iterative method (STIM).The fractional derivatives are represented in the terms of Caputo. Analytical outcomes are obtained in the form of a converging series with easily computable components and are shown graphically. The results of the study suggest that the approach is simple to implement and very attractive in terms of computation.

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Self-similar characteristics of neural networks based on Fokker–Planck equation

Cited by 11 publications

References 11 publications

Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method

Dynamical Study of Fokker-Planck Equations by Using Optimal Homotopy Asymptotic Method

Analytical Solution of Space-Time Fractional Fokker-Planck Equation by Homotopy Perturbation Sumudu Transform Method

An efficient analytical approach for solving fractional Fokker-Planck equations

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