RECENT APPLICATIONS OF FRACTIONAL CALCULUS TO SCIENCE AND ENGINEERING

By Lokenath Debnath, R. Feynman. 2003

778 citations recorded by the source corpus.

This paper deals with recent applications of fractional calculus to dynamical systems in control theory, electrical circuits with fractance, generalized voltage divider, viscoelasticity, fractional-order multipoles in electromagnetism, electrochemistry, tracer in fluid flows, and model of neurons in biology. Special attention is given to numerical computation of fractional derivatives and integrals.

Subfields: Mathematical Physics, Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/84eed3d927e593f5839f459b3e2daedb77fdc839

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In Numerical Analysis

Citations in the corpus

A Fractional Order SEIR Model with Density Dependent Death Rate ABSTRACT | FULL TEXT (2011, background): “In recent years, it has turned out that many phenomena in different fields can be described very successfully by the models using fractional order differential equations [1,2,4,6].”
Fractional Differential Equations with Mixed Boundary Conditions (2017, methodology): “Fractional differential equations have been used to model more efficiently some real-life phenomena like viscoelasticity [12], electrical circuits [16], electromagnetism [10], in chemistry [9], and sound propagation [11] and has attracted the attention of numerous researchers.”
On more general forms of proportional fractional operators (2019, background): “Here, we invite the readers to read [1, 2, 3, 4, 5, 6] and the reference cited in these books.”
Lyapunov functions for fractional-order systems in biology: Methods and applications (2020, background): “uring the last decades, FC has gained popularity and importance in diverse ﬁelds of science and engineering, including biology, physics, chemistry, engineering, ﬁnance, and control theory, see, e.g., [15, 17, 18, 25, 30, 53, 65]. Recently, several works have appeared in the literature that deal with”
Robust Stability and Stabilization of Fractional-Order Interval Systems: An LMI Approach (2009, neutral): “[ 4 ] L. Rosier, “Homogeneous lyapunov function for homogeneous contin-”
A numerical approach based on Legendre orthonormal polynomials for numerical solutions of fractional optimal control problems (2017, background): “…modeling (Benson et al., 2013), bioengineering (Magin, 2004), continuum mechanics (Mainardi, 1997), colored noise (Mandelbrot, 1967) and others (see Debnath, 2003; Bohannan, 2008; Das, 2008; Dalir and Bashour, 2010; Dzielinski et al., 2010; Hilfer, 2012; Jiang and Ding, 2013; Machado et al., 2013;…”
Heat transfer analysis in a second grade fluid over and oscillating vertical plate using fractional Caputo–Fabrizio derivatives (2016, background): “sa past for the study of viscoelastic materials such as polymers in the glass transition and in the glassy state [2].”
Galerkin Projections and Finite Elements for Fractional Order Derivatives (2006, neutral): “, [5–8]).”
Stability and stabilization of fractional-order linear systems with convex polytopic uncertainties (2012, background): “Recently, fractional-order control systems have attracted increasing interest [6],[10],[12],[13],[14],[18],[19],[22],[33].”
Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders (2012, neutral): “Key words: linear system, continuous-time, fractional, stability, Mikhailov criterion.”
Practical stability and asymptotic stability of positive fractional 2D linear systems (2009, background): “Linear matrix inequality (LMI) approaches to checking the stability of positive 2D systems have been proposed in [32, 33].”
Studies on fractional order differentiators and integrators: A survey (2011, background): “Debnath [11] has summarized the application of fractional calculus in various fields of science and engineering.”