scholarly journals Random walk models approximating symmetric space-fractional diffusion processes

2001 ◽  
pp. 120-145 ◽  
Author(s):  
Rudolf Gorenflo ◽  
Francesco Mainardi
Keyword(s):  
Random Walk ◽  
Symmetric Space ◽  
Diffusion Processes ◽  
Fractional Diffusion

Continuous time random walk models associated with distributed order diffusion equations

2015 ◽  
Vol 18 (3) ◽  
Author(s):  
Sabir Umarov
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Diffusion Processes ◽  
Stability Index ◽  
Fractional Diffusion ◽  
Diffusion Equations ◽  
Analytic Method ◽  
Fractional Diffusion Equations ◽  
The Stability ◽  
Distributed Order

AbstractIn this paper continuous time and discrete random walk models approximating diffusion processes associated with time-fractional and spacedistributed order differential equations are studied. Stochastic processes associated with the considered equations represent time-changed processes, where the time-change process is the inverse to a Levy’s stable subordinator with the stability index β ∈ (0, 1). In the paper the convergence of modeled continuous time and discrete random walks to time-changed processes associated with distributed order fractional diffusion equations are proved using an analytic method.

scholarly journals Integrated Time-Fractional Diffusion Processes for Fractional-Order Chaos-Based Image Encryption

Sensors ◽  
2021 ◽  
Vol 21 (20) ◽  
pp. 6838
Author(s):  
Fudong Ge ◽  
Zufa Qin ◽  
YangQuan Chen
Keyword(s):  
Boundary Conditions ◽  
Image Encryption ◽  
Fractional Order ◽  
Diffusion Processes ◽  
Fractional Diffusion ◽  
Spatiotemporal Chaos ◽  
Diffusion System ◽  
Encryption Algorithm ◽  
Secret Key ◽  
Image Encryption Algorithm

The purpose of this paper is to explore a novel image encryption algorithm that is developed by combining the fractional-order Chua’s system and the 1D time-fractional diffusion system of order α∈(0,1]. To this end, we first discuss basic properties of the fractional-order Chua’s system and the 1D time-fractional diffusion system. After these, a new spatiotemporal chaos-based cryptosystem is proposed by designing the chaotic sequence of the fractional-order Chua’s system as the initial condition and the boundary conditions of the studied time-fractional diffusion system. It is shown that the proposed image encryption algorithm can gain excellent encryption performance with the properties of larger secret key space, higher sensitivity to initial-boundary conditions, better random-like sequence and faster encryption speed. Efficiency and reliability of the given encryption algorithm are finally illustrated by a computer experiment with detailed security analysis.

CONTINUOUS TIME RANDOM WALK AND TIME FRACTIONAL DIFFUSION: A NUMERICAL COMPARISON BETWEEN THE FUNDAMENTAL SOLUTIONS

2005 ◽  
Vol 05 (02) ◽  
pp. L291-L297 ◽  
Author(s):  
FRANCESCO MAINARDI ◽  
ALESSANDRO VIVOLI ◽  
RUDOLF GORENFLO
Keyword(s):  
Random Walk ◽  
Continuous Time ◽  
Fundamental Solutions ◽  
Fractional Diffusion ◽  
Continuous Time Random Walk ◽  
Diffusion Limit ◽  
Numerical Comparison ◽  
Time Fractional Diffusion Equation ◽  
Quality Of Approximation

We consider the basic models for anomalous transport provided by the integral equation for continuous time random walk (CTRW) and by the time fractional diffusion equation to which the previous equation is known to reduce in the diffusion limit. We compare the corresponding fundamental solutions of these equations, in order to investigate numerically the increasing quality of approximation with advancing time.

Regional Analysis of Time-Fractional Diffusion Processes

2018 ◽  
Author(s):  
Fudong Ge ◽  
YangQuan Chen ◽  
Chunhai Kou
Keyword(s):  
Diffusion Processes ◽  
Regional Analysis ◽  
Fractional Diffusion
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