Fractional Calculus in Bioengineering

By B. West. 2007

1,396 citations recorded by the source corpus.

Subfields: Control and Systems Engineering, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/2e246bff382bf6fc38b0ecfb0b5df1b1bfdab5b9

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In Control and Systems Engineering

In Modeling and Simulation

In Numerical Analysis

Citations in the corpus

Numerical solution of fractional Sturm-Liouville equation in integral form (2014, neutral): “The fractional differential equations, both ordinary and partial ones, are very useful tools for modelling many phenomena in physics, mechanics, control theory, biochemistry, bioengineering and economics [10, 12, 21, 22, 24, 38].”
New aspects of time fractional optimal control problems within operators with nonsingular kernel (2020, background): “Moreover, fractional calculus in continuous and discrete cases [33, 5, 4, 11, 7, 6, 1, 9, 2, 3] have been applied to physics [26], bioengineering [42], optics [24], fluid flow [21], energy systems [37] and biology [56, 54, 50, 47, 31, 30].”
A Gronwall inequality for a general Caputo fractional operator (2017, background): “1 Introduction Fractional calculus is an important subject with numerous applications to different fields outside mathematics like physics [8, 21, 29], chemistry [4, 5, 14], biology [3, 20, 27, 30], engineering [9, 10, 24, 28], etc.”
Existence and Hyers‐Ulam stability of fractional nonlinear impulsive switched coupled evolution equations (2018, neutral): “Consider a closed ball Br = {(p, q) ∈ E ∶ ||(p, q)|| ≤ r with ||p|| ≤ r 2 , ||q|| ≤ r 2} ⊂ E, where r ≥ |p0| + |q0| + μ + ν 1 − ζ1 , (6) and define operators ϝ = (ϝ1, ϝ2),G = (G1,G2) on Br as ⎧⎪⎪⎨⎪⎪⎪⎪⎩ ϝ1p(t) = p0 − φ(p) + m ∑”
On fractional derivatives with exponential kernel and their discrete versions (2016, background): “1 Introduction The techniques of the fractional calculus are applied successfully in many branches of science and engineering [1, 2, 3, 4, 7].”
TEMPERED FRACTIONAL CALCULUS (2015, background): “They are now used to model a wide variety of problems in physics [24, 35,38,50,51,55,65], finance [23,27,37,42,60,61], biology [2,4,22,26,36], and hydrology [1,7,8,15,17,62].”
A Note on Fractional Order Derivatives and Table of Fractional Derivatives of Some Special Functions (2013, methodology): “It has been recognized as a powerful modelling approach in the fields of viscoelasticity [17–32] viscoelastic deformation [28], viscous fluid [29] and anomalous diffusion [30].”
On exact solutions of a class of fractional Euler–Lagrange equations (2007, background): “1 Introduction Fractional calculus is an emerging fields and during the last decades it represents an alternative tool to solve several problems from various fields [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11].”
Spline collocation methods for seismic analysis of multiple degree of freedom systems with visco-elastic dampers using fractional models (2020, background): “It generalizes the notions of integer-order differentiation and n-fold integration (Atangana and Baleanu, 2016; Baleanu et al., 2011, 2012; Diethelm, 2010; Edwards et al., 2002; Gemant, 1936; Gorenflo and Mainardi, 1997; Kilbas et al., 2006; Magin, 2006; Podlubny, 1999; Sabatier et al., 2007; Tenrei”
Tuning and implementation methods for fractional-order controllers (2012, background): “There is a number of applications in various areas, that were already published, for instance [6, 13, 17, 20, 23, 31].”
A unified Petrov-Galerkin spectral method for fractional PDEs (2015, background): “operators appear as attractive and potentially powerful modeling tools in many areas such as viscoelastic materials [3,4], porous or fractured media [5], fluid mechanics [6–8], bioengineering [9], and anomalous diffusion (nonMarkovian) processes [10,11].”
Fractional Sturm-Liouville eigen-problems: Theory and numerical approximation (2013, background): “Over the last decade, it has been demonstrated that many systems in science and engineering can be modeled more accurately by employing fractional-order rather than integer-order derivatives [6] [7] [8].”
An efficient approximate method for solving delay fractional optimal control problems (2016, background): “Fractional-order dynamics appear in several problems in science and engineering such as viscoelastic materials [5], economics [6], continuum and statistical mechanics [27], solid mechanics [36], bioengineering [26], dynamics of interfaces between nanoparticles and substrates [9].”
On a Regular Fractional Sturm-Liouville Problem with derivatives of order in (0,1) (2012, neutral): “In recent years, it has been demonstrated that many systems in different fields of science and engineering can be modeled more accurately using fractional derivatives [5]–[9].”