A closed form expression for the Gaussian–based Caputo–Fabrizio fractional derivative for signal processing applications

Cruz–Duarte, Jorge M.; Rosales, J. J.; Correa-Cely, Rodrigo; García-Pérez, Arturo; Aviña-Cervantes, Juan Gabriel

doi:10.1016/j.cnsns.2018.01.020

Cited by 72 publications

(35 citation statements)

References 32 publications

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“…Recently, many new fractional-order operator types have been introduced to the literature by some scholars, and established its fundamental properties [1][2][3][4][5][6]. Fractional theory is widely used to explain many properties of phenomena such as nanotechnology [7], optics [8], human diseases [9], chaos theory [10], and others . As an example, the tumor-immune surveillance model has been investigated in [33].…”

Section: Introductionmentioning

confidence: 99%

New Numerical Results for the Time-Fractional Phi-Four Equation Using a Novel Analytical Approach

et al. 2020

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This manuscript investigates the fractional Phi-four equation by using q -homotopy analysis transform method ( q -HATM) numerically. The Phi-four equation is obtained from one of the special cases of the Klein-Gordon model. Moreover, it is used to model the kink and anti-kink solitary wave interactions arising in nuclear particle physics and biological structures for the last several decades. The proposed technique is composed of Laplace transform and q -homotopy analysis techniques, and fractional derivative defined in the sense of Caputo. For the governing fractional-order model, the Banach’s fixed point hypothesis is studied to establish the existence and uniqueness of the achieved solution. To illustrate and validate the effectiveness of the projected algorithm, we analyze the considered model in terms of arbitrary order with two distinct cases and also introduce corresponding numerical simulation. Moreover, the physical behaviors of the obtained solutions with respect to fractional-order are presented via various simulations.

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Section: Introductionmentioning

confidence: 99%

New Numerical Results for the Time-Fractional Phi-Four Equation Using a Novel Analytical Approach

et al. 2020

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“…The new notion is receiving an increasing of interest. For example, in [24] a numerical approach based on optimization theory and Ritz's method is developed to deal with Caputo-Fabrizio Fokker-Planck equations; applications in linear viscoelasticity are presented in [3]; while practical signal processing problems are investigated in [22]. Moreover, in [33] the authors show that the Caputo-Fabrizio operator may be a simple and efficient way for incorporating different structural aspects into the system, opening new possibilities for modeling and investigating anomalous diffusive processes.…”

Section: Introductionmentioning

confidence: 99%

Solutions of systems with the Caputo–Fabrizio fractional delta derivative on time scales

Mozyrska

Torres

Wyrwas

2019

Nonlinear Analysis: Hybrid Systems

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Caputo-Fabrizio fractional delta derivatives on an arbitrary time scale are presented. When the time scale is chosen to be the set of real numbers, then the Caputo-Fabrizio fractional derivative is recovered. For isolated or partly continuous and partly discrete, i.e., hybrid time scales, one gets new fractional operators. We concentrate on the behavior of solutions to initial value problems with the Caputo-Fabrizio fractional delta derivative on an arbitrary time scale. In particular, the exponential stability of linear systems is studied. A necessary and sufficient condition for the exponential stability of linear systems with the Caputo-Fabrizio fractional delta derivative on time scales is presented. By considering a suitable fractional dynamic equation and the Laplace transform on time scales, we also propose a proper definition of Caputo-Fabrizio fractional integral on time scales. Finally, by using the Banach fixed point theorem, we prove existence and uniqueness of solution to a nonlinear initial value problem with the Caputo-Fabrizio fractional delta derivative on time scales.

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“…It is now established experimentally as well as theoretically that the mathematical models derived with the help of fractional order derivatives simulate certain physical phenomenon more realistically, particularly for the systems wherein the hereditary effects are important as they depend on the past conditions. Recently fractional models have been developed and employed in many fields of science and engineering like fluid dynamics, electromagnetic, biopopulation models, viscoelasticity, optics, electro-chemistry, and signal processing in order to establish behavior of several physical quantities; see, for example, [28][29][30][31] and the references therein. For accurate modeling of damping, fractional models are used; the reader is referred to study the articles [32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Mixed Convection Magnetohydrodynamics Flow of a Nanofluid with Heat Transfer: A Numerical Study

Khan

Rasheed

2019

Mathematical Problems in Engineering

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In this paper we have studied the magnetohydrodynamic (MHD) mixed convection Maxwell flow of an incompressible nanofluid with magnetic field and heat transfer over a moving plate aligned horizontally. Thermal radiation has also been applied in order to investigate its effects on velocity and temperature variations in the fluid. The Caputo time derivative has been employed to derive the mathematical model. A numerical solution has been obtained using finite difference discretization along with L1-algorithm. Fractional and other pertinent physical fluid parameters like magnetic field parameter, thermal radiation, effect on velocity, and temperature distribution are analyzed and demonstrated through graphs.

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A closed form expression for the Gaussian–based Caputo–Fabrizio fractional derivative for signal processing applications

Cited by 72 publications

References 32 publications

New Numerical Results for the Time-Fractional Phi-Four Equation Using a Novel Analytical Approach

New Numerical Results for the Time-Fractional Phi-Four Equation Using a Novel Analytical Approach

Solutions of systems with the Caputo–Fabrizio fractional delta derivative on time scales

Mixed Convection Magnetohydrodynamics Flow of a Nanofluid with Heat Transfer: A Numerical Study

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