Results 11 to 20 of about 6,876 (298)
Fractional Mass-Spring-Damper System Described by Generalized Fractional Order Derivatives
Fractal and Fractional, 2019 This paper proposes novel analytical solutions of the mass-spring-damper systems described by certain generalized fractional derivatives. The Liouville−Caputo left generalized fractional derivative and the left generalized fractional derivative ...
Ndolane Sene +1 more
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ANALYSIS OF DENGUE FEVER OUTBREAK BY GENERALIZED FRACTIONAL DERIVATIVE
Fractals, 2020 In this paper, we use the generalized fractional derivative in order to study the fractional differential equation associated with a fractional Gaussian model. Moreover, we propose new properties of generalized differential and integral operators. As a practical application, we estimate the order of the derivative of the fractional Gaussian models by ...
Paul Bosch +3 more
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A Gronwall inequality via the generalized proportional fractional derivative with applications
Journal of Inequalities and Applications, 2019 In this paper, we provide a new version for the Gronwall inequality in the frame of the generalized proportional fractional derivative. Prior to the main results, we introduce the generalized proportional fractional derivative and expose some of its ...
Jehad Alzabut +3 more
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Exact results for a fractional derivative of elementary functions
SciPost Physics, 2018 We present exact analytical results for the Caputo fractional derivative of a wide class of elementary functions, including trigonometric and inverse trigonometric, hyperbolic and inverse hyperbolic, Gaussian, quartic Gaussian, and Lorentzian ...
Gavriil Shchedrin, Nathanael C. Smith, Anastasia Gladkina, Lincoln D. Carr
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Advances in Difference Equations, 2019 We introduce nonlinear fractional BVPs including a generalized proportional derivatives with nonlocal multipoint and substrip boundary conditions. The nonlinearities are defined on the Orlicz space and depend on the unknown function and its generalized ...
Wafa Shammakh, Hadeel Z. Alzumi
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International Journal of Analysis and Applications, 2018 We introduce a truncated $M$-fractional derivative type for $\alpha$-differentiable functions that generalizes four other fractional derivatives types recently introduced by Khalil et al., Katugampola and Sousa et al., the so-called conformable ...
J. Vanterler da C. Sousa +1 more
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A Generalized Definition of the Fractional Derivative with Applications
Mathematical Problems in Engineering, 2021 A generalized fractional derivative (GFD) definition is proposed in this work. For a differentiable function expanded by a Taylor series, we show that D α
M. Abu-Shady, Mohammed K. A. Kaabar
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Mathematics, 2022 The generalized proportional Caputo fractional derivative is a comparatively new type of derivative that is a generalization of the classical Caputo fractional derivative, and it gives more opportunities to adequately model complex phenomena in physics ...
Ravi Agarwal +2 more
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Generalized Hamilton's principle with fractional derivatives [PDF]
Journal of Physics A: Mathematical and Theoretical, 2010 We generalize Hamilton's principle with fractional derivatives in Lagrangian $L(t,y(t),{}_0D_t^\al y(t),α)$ so that the function $y$ and the order of fractional derivative $α$ are varied in the minimization procedure. We derive stationarity conditions and discuss them through several examples.
Atanacković, Teodor +3 more
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On the (k,s)-Hilfer-Prabhakar Fractional Derivative With Applications to Mathematical Physics
Frontiers in Physics, 2020 In this paper we introduce the (k, s)-Hilfer-Prabhakar fractional derivative and discuss its properties. We find the generalized Laplace transform of this newly proposed operator. As an application, we develop the generalized fractional model of the free-
Muhammad Samraiz +4 more
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