Dynamical properties of a meminductor chaotic system with fractal–fractional power law operator

Li, Peiluan; Han, Liqin; Xu, Changjin; Peng, Xueqing; Rahman, Mati ur; Shi, Sairu

doi:10.1016/j.chaos.2023.114040

Cited by 14 publications

(2 citation statements)

References 58 publications

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“…The application of fractional calculus in biological models allows for a more accurate representation of system dynamics, particularly in situ ations including memory effects and non-local interactions [5][6][7], and [8]. In [9] the authors investigated the fractional tuberculosis model with the effect of an imperfect vaccine and exogenous factors under the MittagLeffler kernel and for more details refer [10,11], and [12]. Furthermore, fractional integro differential equations (FIDEs) are a subject that several academics have developed in recent years.…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of fuzzy fractional volterra integro differential equations with boundary conditions

Agilan,

Parthiban

2024

Phys. Scr.

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In this study, the boundary value problem of fuzzy fractional nonlinear Volterra integro differential equations of order 1 < ρ ≤ 2 is addressed. Fuzzy fractional derivatives are defined in the Caputo sense. To show the existence result, the Krasnoselkii theorem from the theory of fixed points is used, where as the well-known contraction mapping concept is utilized in order to show the solution is unique to the proposed problem. Moreover, a novel Adomian decomposition method is utilized to get numerical solution; the approach behind deriving the solution is from Adomian polynomials, and it is organized according to the recursive relation that is obtained. The proposed method significantly decreases the numerical computations by obtaining solutions without the need of discretization or constrictive assumptions. According to the results, there is substantial agreement between the seriessolutions produced by the fuzzy Adomian decomposition method. Finally, using MATLAB, the symmetry between the lower and upper-cut representations of the fuzzy solutions is demonstrated in the numerical result.

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Section: Introductionmentioning

confidence: 99%

Numerical solution of fuzzy fractional volterra integro differential equations with boundary conditions

Agilan,

Parthiban

2024

Phys. Scr.

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“…Moreover, the wavelet technique is employed to calculate the solution of a complex plane NVHIEq and a mixed VFHIEq of the second type. Several additional investigations, including those referenced as [11][12][13][14][15][16][17][18][19][20], have also examined comparable subjects.…”

Section: Introductionmentioning

confidence: 99%

A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space

Shammaky,

Youssef,

Abdou

et al. 2023

Fractal Fract

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This work aims to explore the solution of a nonlinear fractional integro-differential equation in the complex domain through the utilization of both analytical and numerical approaches. The demonstration of the existence and uniqueness of a solution is established under certain appropriate conditions with the use of Banach fixed point theorems. To date, no research effort has been undertaken to look into the solution of this integro equation, particularly due to its fractional order specification within the complex plane. The validation of the proposed methodology was performed by utilizing a novel strategy that involves implementing the Rationalized Haar wavelet numerical method with the application of the Bernoulli polynomial technique. The primary reason for choosing the proposed technique lies in its ability to transform the solution of the given nonlinear fractional integro-differential equation into a representation that corresponds to a linear system of algebraic equations. Furthermore, we conduct a comparative analysis between the outcomes obtained from the suggested method and those derived from the rationalized Haar wavelet method without employing any shared mathematical methodologies. In order to evaluate the precision and effectiveness of the proposed method, a series of numerical examples have been developed.

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Effective methods for numerical analysis of the simplest chaotic circuit model with Atangana–Baleanu Caputo fractional derivative

Alzahrani,

Saadeh,

Abdoon

et al. 2024

J Eng Math

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Dynamical properties of a meminductor chaotic system with fractal–fractional power law operator

Cited by 14 publications

References 58 publications

Numerical solution of fuzzy fractional volterra integro differential equations with boundary conditions

Numerical solution of fuzzy fractional volterra integro differential equations with boundary conditions

A New Technique for Solving a Nonlinear Integro-Differential Equation with Fractional Order in Complex Space

Effective methods for numerical analysis of the simplest chaotic circuit model with Atangana–Baleanu Caputo fractional derivative

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