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Fractal Fract, Volume 2, Issue 2 (June 2018)

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Open AccessEditorial Fractional Dynamics
Fractal Fract 2018, 2(2), 19; https://doi.org/10.3390/fractalfract2020019
Received: 5 June 2018 / Accepted: 11 June 2018 / Published: 17 June 2018
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(This article belongs to the Special Issue Fractional Dynamics)
Open AccessArticle Analytical Solutions to Fractional Fluid Flow and Oscillatory Process Models
Fractal Fract 2018, 2(2), 18; https://doi.org/10.3390/fractalfract2020018
Received: 5 April 2018 / Revised: 21 May 2018 / Accepted: 24 May 2018 / Published: 27 May 2018
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Abstract
In this paper, we provide solutions to the general fractional Caputo-type differential equation models for the dynamics of a sphere immersed in an incompressible viscous fluid and oscillatory process with fractional damping using Laplace transform method. We study the effects of fixing one
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In this paper, we provide solutions to the general fractional Caputo-type differential equation models for the dynamics of a sphere immersed in an incompressible viscous fluid and oscillatory process with fractional damping using Laplace transform method. We study the effects of fixing one of the fractional indices while varying the other as particular examples. We conclude this article by explaining the dynamics of the solutions of the models. Full article
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Open AccessArticle Lyapunov Characterization of the Fractional Nonlinear Systems with Exogenous Input
Fractal Fract 2018, 2(2), 17; https://doi.org/10.3390/fractalfract2020017
Received: 31 March 2018 / Revised: 25 April 2018 / Accepted: 27 April 2018 / Published: 2 May 2018
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Abstract
This paper deals with a Lyapunov characterization of the conditional Mittag-Leffler stability and conditional asymptotic stability of the fractional nonlinear systems with exogenous input. A particular class of the fractional nonlinear systems is studied. The paper contributes to giving in particular the Lyapunov
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This paper deals with a Lyapunov characterization of the conditional Mittag-Leffler stability and conditional asymptotic stability of the fractional nonlinear systems with exogenous input. A particular class of the fractional nonlinear systems is studied. The paper contributes to giving in particular the Lyapunov characterization of fractional linear systems and fractional bilinear systems with exogenous input. Full article
Open AccessEditorial The Craft of Fractional Modeling in Science and Engineering 2017
Fractal Fract 2018, 2(2), 16; https://doi.org/10.3390/fractalfract2020016
Received: 12 April 2018 / Revised: 12 April 2018 / Accepted: 13 April 2018 / Published: 15 April 2018
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