Fractional calculus models of complex dynamics in biological tissues

By Richard L. Magin. Computers and Mathematics with Applications, 2010

998 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Modeling and Simulation, Physical and Theoretical Chemistry

View Paper: https://www.semanticscholar.org/paper/384c2c8a5119e033584dd79010b3adc8bd7afabb

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In Biomedical Engineering

In Modeling and Simulation

In Physical and Theoretical Chemistry

Citations in the corpus

GEGENBAUER WAVELETS OPERATIONAL MATRIX METHOD FOR FRACTIONAL DIFFERENTIAL EQUATIONS (2015, methodology): “Introduction Fractional differential equation is the generalization of the ordinary differential equation and is used to model the problems in many areas of science and engineering such as fluid mechanics [19], dynamic of viscoelastic materials [20], biosciences [23], electromagnetism [15] and conti”
Extended Riemann-Liouville fractional derivative operator and its applications (2015, background): “…extended Beta function given by Srivastava et al. [22] and investigate its various (potentially) useful and (presumably) new properties and formulas, for example, integral representations, Mellin transforms, generating functions, and the extended fractional derivative formulas for some familiar…”
On the ψ-Hilfer fractional derivative (2017, background): “The importance of fractional calculus growth is notable not only in pure and applied mathematics but also in physics, chemistry, engineering, biology, and other [3, 4, 5, 6, 7, 8, 9, 10, 11].”
A novel Jacobi operational matrix for numerical solution of multi-term variable-order fractional differential equations (2020, methodology): “These applications are used in several fields of engineering and science such as biology [8], dynamics [9], physics [10,11], medicine [12], fluid [13] and others [14–16].”
On the existence of solutions of fractional integro-differential equations (2011, positive): “Besides the mentioned books, there are several papers about the applications of the fractional calculus in signal processing, complex dynamics in biological tissues, viscoelastic materials, thermal systems and heat conduction (for example, see [25]-[27], [34] and [37]).”
Existence of a weak solution for fractional Euler-Lagrange equations (2012, background): “Nevertheless, during the last two decades, fractional calculus has attracted the attention of many researchers and it has been successfully applied in various areas like computational biology [21] or economy [9].”
Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach ☆ (2013, background): “Introduction In the past few decades, much attention has been drawn for the study of fractional calculus [1–7].”