Fractal electrodynamics via non-integer dimensional space approach

Tarasov, Vasily E.

doi:10.1016/j.physleta.2015.06.032

Cited by 56 publications

(9 citation statements)

References 39 publications

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“…Fractional derivatives, which are a generalization of classical derivatives have been extensively used in describing and solving integral equations, ordinary and partial differential equations in applied sciences such as fluid mechanics, diffusive transport, electrical networks, electrodynamics, nonlinear control theory, signal processing, nonlinear biological systems, astrophysics, among others [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Solís-Pérez

Gómez-Aguilar

Băleanu

et al. 2018

Entropy

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This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and β-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and β-conformable attractors are provided to illustrate the effectiveness of the proposed method.

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Section: Introductionmentioning

confidence: 99%

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Solís-Pérez

Gómez-Aguilar

Băleanu

et al. 2018

Entropy

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“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14] The main idea of using the fractional differentiation lies in the property of the fractional-order derivatives to describe memory effects. In the last 30 years, this subject has been extended in various directions such as fluid dynamics, tribology, electrochemistry, vibrations, finance, the design of optimal control systems, diffusion, geophysics, thermoelectricity, reaction-diffusion equations, signal processing, among others.…”

Section: Introductionmentioning

confidence: 99%

“…In the last 30 years, this subject has been extended in various directions such as fluid dynamics, tribology, electrochemistry, vibrations, finance, the design of optimal control systems, diffusion, geophysics, thermoelectricity, reaction-diffusion equations, signal processing, among others. [1][2][3][4][5][6][7][8][9][10][11][12][13][14] The main idea of using the fractional differentiation lies in the property of the fractional-order derivatives to describe memory effects. Derivatives and integrals of fractional-order consider the system memory, hereditary properties, and nonlocal distributed effects; these effects are essential for describing real-world problems.…”

Section: Introductionmentioning

confidence: 99%

Fractional operator without singular kernel: Applications to linear electrical circuits

Morales‐Delgado

Gómez-Aguilar

Taneco-Hernández

et al. 2018

Circuit Theory & Apps

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This paper presents the analytical solutions of fractional linear electrical systems by using the Caputo-Fabrizio fractional-order operator in Liouville-Caputo sense. This novel operator involves an exponential kernel without singularities. The fractional equations were solved analytically by using the properties of Laplace transform operator, as well as the convolution theorem. To validate the analytical solutions, numerical simulations were carried out. KEYWORDSCaputo-Fabrizio fractional operator, exponential decay law kernel, fractional linear electrical circuits, Laplace transform 2394

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“…Recently, fractional calculus (FC) was considered to solve a class of the fractal problems in mathematical physics, [24][25][26][27][28] mechanics, [29][30][31] heat, 32 biology 33 and others. [34][35][36][37] There is an alternative operator (called local FC) to model the local FODEs in fractal electric circuits, 38 free damped vibrations, 39 shallow water surfaces 40 and populations.…”

Section: Introductionmentioning

confidence: 99%

Non-Differentiable Exact Solutions for the Nonlinear Odes Defined on Fractal Sets

2017

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In the present paper, a family of the special functions via the celebrated Mittag-Leffler function defined on the Cantor sets is investigated. The nonlinear local fractional ODEs (NLFODEs) are presented by following the rules of local fractional derivative (LFD). The exact solutions for these problems are also discussed with the aid of the non-differentiable charts on Cantor sets. The obtained results are important for describing the characteristics of the fractal special functions.

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Fractal electrodynamics via non-integer dimensional space approach

Cited by 56 publications

References 39 publications

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors

Fractional operator without singular kernel: Applications to linear electrical circuits

Non-Differentiable Exact Solutions for the Nonlinear Odes Defined on Fractal Sets

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