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1992•Journal of Mathematical PhysicsRequires access

A Fokker–Planck equation of fractional order with respect to time

Guy Jumarie

Open publisher page 63 citations

Abstract

By combining the maximum entropy principle with some considerations related to derivatives of fractional order, one is led to suggest a Fokker–Planck of fractional order with respect to time, which could be related to dynamical systems subject to fractional Brownian motion. The relation with the process associated with the equation ∂p/∂t=(−1)n+1∂2np/∂x2n is exhibited.

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What this paper is about

By combining the maximum entropy principle with some considerations related to derivatives of fractional order, one is led to suggest a Fokker–Planck of fractional order with respect to time, which could be related to dynamical systems subject to fractional Brownian motion. The relation with the process associated with the equation ∂p/∂t=(−1)n+1∂2np/∂x2n is exhibited.

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OpenAlex reports 63 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

By combining the maximum entropy principle with some considerations related to derivatives of fractional order, one is led to suggest a Fokker–Planck of fractional order with respect to time, which could be related to dynamical systems subject to fractional Brownian motion. The relation with the process associated with the equation ∂p/∂t=(−1)n+1∂2np/∂x2n is exhibited.

Key concepts: Fokker–Planck equation, Fractional Brownian motion, Mathematics, Fractional calculus, Order (exchange), Brownian motion, Mathematical physics, Principle of maximum entropy

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