Variable-order fractional differential operators in anomalous diffusion modeling

By Hongguang Sun, Wen Chen, YangQuan Chen. 2009

599 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/af5024317997e36491e56e0553e044df8c5f887b

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Citations in the corpus

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A variable-order time-fractional derivative model for chloride ions sub-diffusion in concrete structures (2012, background): “where p(t) is a function with respect to variable t [29].”
Adaptive finite element method for fractional differential equations using hierarchical matrices (2016, background): “Numerical methods for differential equations involving fractional derivatives either in time or space have been studied widely since they have various new scientific applications [29, 31, 34, 35, 5, 32, 28].”
Application of fractional calculus in modelling ballast deformation under cyclic loading (2017, methodology): “151 Geotechnical applications using fractional calculus include the creep and relaxation 152 behaviour of composite soil [17], the time dependence of Poisson’s ratio [18], the strain 153 hardening and softening behaviour of sand and clay under monotonic loading [19], the 154 vibration of rail pads [”
Use of a variable-index fractional-derivative model to capture transient dispersion in heterogeneous media. (2014, background): “…fractional derivative, which is also called the variable-order fractional derivative (Chechkin et al., 2005; Coimbra, 2003; Samko and Ross, 1993), depicts the influence of time-dependent memory and variable spatial correlation of medium heterogeneity on tracer dynamics (Sun et al., 2009, 2011).”
Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach ☆ (2013, unknown): “Especially, the study on the dynamics of fractional-order differential systems has attracted increasing affection from many researchers [8–13].”
A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions (2013, methodology): “In addition, when we consider diffusion process in porous medium, if the medium structure or external field changes with time, in this situation, the constant-order fractional diffusion equation model cannot be used to well characterize such phenomenon [23, 24].”
Adaptive fractional-order switching-type control method design for 3D fractional-order nonlinear systems (2015, background): “The reason is that the mathematical technology for FO operators has rapidly grown [2–7] and FO modeling has been wildly used in real-world applications [8,9].”