Local fractional Fokker-Planck equation

Abstract

New kind of differential equations, called local fractional differential equations, has been proposed for the first time. They involve local fractional derivatives introduced recently. Such equations appear to be suitable to deal with phenomena taking place in fractal space and time. A local fractional analog of Fokker-Planck equation has been derived starting from the Chapman-Kolmogorov condition. Such an equation is solved, with a specific choice of the transition probability, and shown to give rise to subdiffusive behavior.

4 pages, Revtex

References in corpus (1)

• Holder exponents of irregular signals and local fractional derivatives

Cited by in corpus (27)

• Levy Flights in External Force Fields: Langevin and Fractional Fokker-Planck Equations, and their Solutions
• Fractional Variational Iteration Method for Fractional Nonlinear Differential Equations
• A physically based connection between fractional calculus and fractal geometry
• A Fractional Calculus on Arbitrary Time Scales: Fractional Differentiation and Fractional Integration
• On a connection between a class of q-deformed algebras and the Hausdorff derivative in a medium with fractal metric
• Variational Approach and Deformed Derivatives
• Generalized Local Fractional Taylor's Formula with Local Fractional Derivative
• Local Fractional Derivatives of Differentiable Functions are Integer-order Derivatives or Zero
• Fractional velocity as a tool for the study of non-linear problems
• Feynman-Kac equation revisited
• Expression of Generalized Newton Iteration Method via Generalized Local Fractional Taylor Series
• On the quantum potential
• Fractional derivatives of random walks: Time series with long-time memory
• Optimal error estimates for Legendre expansions of singular functions with fractional derivatives of bounded variation
• Approximate solution to the fractional Lane-Emden type equations
• A Stochastic Description for Extremal Dynamics
• The Colored Noise of Magnetic Monopoles: Subdiffusion in a Coevolving Vacuum and Spin Ice Exponents
• Generalized Tu Formula and Hamilton Structures of Fractional Soliton Equation Hierarchy
• Fractional Trigonometric Functions in Complex-valued Space: Applications of Complex Number to Local Fractional Calculus of Complex Function
• Anomalous g-Factors for Charged Leptons in a Fractional Coarse-Grained Approach
• Separable local fractional differential equations
• The Exact Spectral Derivative Discretization Finite Difference (ESDDFD) Method for Wave Models: A Universal Wave View Through Natural Fractional / Fractal Derivative Representations (or View Lens Shops for The Exponential Wave Universe)
• Calculus on fractal subsets of real line - I: formulation
• On the conditions for existence and continuity of fractional velocity
• On the Stability of Fractal Differential Equations
• Non-local Integrals and Derivatives on Fractal Sets with Applications
• Diffusion on Fractal Cesàro Curve