Applications Of Fractional Calculus In Physics

By Rudolf Hilfer. 2000

7,083 citations recorded by the source corpus.

Subfields: Fluid Flow and Transfer Processes, Mechanics of Materials, Modeling and Simulation

View Paper: https://www.semanticscholar.org/paper/5aeff09300fcda097719430e0dab6ab1ab3b0264

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In Fluid Flow and Transfer Processes

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Citations in the corpus

Existence of Solutions for Fractional Differential Equations with Multi-point Boundary Conditions at Resonance on a Half-line (2011, background): “Apart from diverse areas of mathematics, fractional differential equations arise in a variety of different areas such as rheology, fluid flows, electrical networks, viscoelasticity, chemical physics, and many other branches of science (see [1, 9, 10, 11, 16, 17, 25] and references cited therein).”
Asymptotic Stability of Fractional Stochastic Neutral Differential Equations with Infinite Delays (2013, background): “On the other hand, recently fractional differential equations have found numerous applications in various fields of science and engineering [6].”
Some Existence and Stability Results for Hilfer-fractional Implicit Differential Equations with Nonlocal Conditions (2018, positive): “(see [15]) The left-sided Hilfer fractional derivative of order 0 < α < 1 and 0 ≤ β ≤ 1 of function f(t) is defined by D 0+ f(t) = ( I β(1−α) 0+ D ( I (1−β)(1−α) 0+ f )) (t), where D := d dt .”
On generalized fractional kinetic equations (2004, background): “The results are obtained in a compact form in terms of generalized Mittag-Leffler functions.”
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].”
Fractional optimal control problems: a pseudo-state-space approach (2011, background): “…role in many areas of science, engineering, and mathematics (Oldham and Spanier, 1974; Miller and Ross, 1993; Samko et al., 1993; Carpinteri and Mainardi, 1997; Rossikhin and Shitikova, 1997; Podlubny, 1999; Hilfer, 2000; West et al., 2003; Magin, 2004; Agrawal et al., 2004; Mehaute et al., 2005).”
Tuning of PID Controllers Based on Bode’s Ideal Transfer Function (2004, background): “In the last years, the area of fractional calculus becomes an active field of research in almost all areas of science and engineering [3–5].”