Fractional Calculus with Applications in Mechanics: Vibrations and Diffusion Processes

By Teodor M. Atanackovic, Stevan Pilipovic, Bogoljub Stankovic, Dušan Zorica. 2014

378 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/cdbf82184c1ef041f89ccb41d25fd640547ad13f

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In Fluid Flow and Transfer Processes

In Mechanics of Materials

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Citations in the corpus

A Caputo fractional derivative of a function with respect to another function (2016, neutral): “For the Riemann–Liouville case, we suggest [7].”
On the Ulam–Hyers–Rassias stability for nonlinear fractional differential equations using the $$\psi $$ψ-Hilfer operator (2017, background): “Fractional differential equations arise naturally in different fields such as biology, engineering, medicine, physics and mathematics [1, 2, 5, 6, 7, 8, 9].”
Fractional Calculus: Quo Vadimus? (Where are we Going?) (2015, result): “We have taken the present occasion, as a compliment to our previous survey [107], to cite books published during the years 2011 [92, 80, 44, 26, 65, 47, 5, 106, 117], 2012 [7, 3, 77, 1, 51, 38, 102, 56, 122, 15, 112, 110, 118], 2013 [14, 18, 89, 29, 36], and 2014 [57, 4, 121, 39, 105, 40, 66, 86, 2,”
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].”
Modeling some real phenomena by fractional differential equations (2015, neutral): “For example, we can find applications of fractional calculus in mechanics [4], engineering [5], viscoelasticity [6], dynamical systems [7], etc.”
On some new properties of fractional derivatives with Mittag-Leffler kernel (2017, background): “For example, they can be used to model controllability [22], viscoelastic flows [25, 12], chaotic systems [33], Stokes problems [46], thermoelasticity [35], several vibration and diffusion processes [8, 39, 6], bioengineering problems [24], and many other complex phenomena.”