Mathematical physiology
Dynamics of complex systems
Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
Dynamical analysis of fractional-order modified logistic model
Computers & Mathematics with Applications
Computers & Mathematics with Applications
Brief paper: Analytical computation of the H2-norm of fractional commensurate transfer functions
Automatica (Journal of IFAC)
A fractional-order model on new experiments of linear viscoelastic creep of Hami Melon
Computers & Mathematics with Applications
The Cattaneo-type time fractional heat conduction equation for laser heating
Computers & Mathematics with Applications
Computer Methods and Programs in Biomedicine
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Fractional (non-integer order) calculus can provide a concise model for the description of the dynamic events that occur in biological tissues. Such a description is important for gaining an understanding of the underlying multiscale processes that occur when, for example, tissues are electrically stimulated or mechanically stressed. The mathematics of fractional calculus has been applied successfully in physics, chemistry, and materials science to describe dielectrics, electrodes and viscoelastic materials over extended ranges of time and frequency. In heat and mass transfer, for example, the half-order fractional integral is the natural mathematical connection between thermal or material gradients and the diffusion of heat or ions. Since the material properties of tissue arise from the nanoscale and microscale architecture of subcellular, cellular, and extracellular networks, the challenge for the bioengineer is to develop new dynamic models that predict macroscale behavior from microscale observations and measurements. In this paper we describe three areas of bioengineering research (bioelectrodes, biomechanics, bioimaging) where fractional calculus is being applied to build these new mathematical models.