A comparative study of constant-order and variable-order fractional models in characterizing memory property of systems

By Hongguang Sun, Wen Chen, H. Wei, Yang Chen. 2011

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Numerical simulation for two-dimensional variable-order fractional nonlinear cable equation (2014, background): “The effect of differences between using constant and variable-order fractional derivatives has been discussed in [33].”
A fractional calculus approach to the dynamic optimization of biological reactive systems. Part I: Fractional models for biological reactions (2014, background): “In addition, many works describe and/or study the nonlocality property and the memory effect of fractional calculus operators (Magin, 2006; Herrmann, 2011; Sun et al., 2011; Constantinescu and Stoicescu, 2011; Du et al., 2013).”
Non standard finite difference method for solving variable order fractional optimal control problems (2017, background): “Sun et al. (2011) studied the investigation of integer order derivative, constant order fractional derivative and two types of variable order fractional derivatives in characterizing the memory property of systems.”
A review on variable-order fractional differential equations: mathematical foundations, physical models, numerical methods and applications (2019, background): “The difference of these two definitions in characterizing the system memory property has been investigated by considering VO fractional relaxation-type differential equation in [106].”