Numerical simulation of fractional-order dynamical systems in noisy environments

Mostaghim, Z. S.; Moghaddam, Behrouz Parsa; Haghgozar, Hossein Samimi

doi:10.1007/s40314-018-0698-z

Cited by 27 publications

(10 citation statements)

References 58 publications

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“…This branch studies the possibility of taking the real number powers of the differentiation and the integration operators. Many physical systems are modeled by fractional partial differential equations, see Moghaddam and Machado (2017) and Mostaghim et al (2018). One of the biggest problems that contain fractional derivatives is the nonlinear TFPIDE.…”

Section: Introductionmentioning

confidence: 99%

Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel

Atta

Youssri

2022

Comp. Appl. Math.

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This research apparatuses an approximate spectral method for the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel (TFPIDE). The main idea of this approach is to set up a new Hilbert space that satisfies the initial and boundary conditions. The new spectral collocation approach is applied to obtain precise numerical approximation using new basis functions based on shifted first-kind Chebyshev polynomials (SCP1K). Furthermore, we support our study by a careful error analysis of the suggested shifted first-kind Chebyshev expansion. The results show that the new approach is very accurate and effective.

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Section: Introductionmentioning

confidence: 99%

Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel

Atta

Youssri

2022

Comp. Appl. Math.

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“…When the mathematical system is a real-world issue throughout in the form of a dynamic system, its state at any moment t may be forecasted. In the analysis and prediction of such systems, the fractional-order calculus has been observed to be a useful tool for comprehending complex dynamical systems having nonlinear properties [17,18].…”

Section: Introductionmentioning

confidence: 99%

On fractional-order symmetric oscillator with offset-boosting control

Rahman

Băleanu

2022

NAMC

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This article analyzes the dynamical evolution of a three-dimensional symmetric oscillator with a fractional Caputo operator. The dynamical properties of the considered model such as equilibria and its stability are also presented. The existence results and uniqueness of solutions for the suggested model are analyzed using the tools from fixed point theory. The symmetric oscillator is analyzed numerically and graphically with various fractional orders. It is observed that the fractional operator has a significant impact on the evolution of the oscillator dynamics showing that the system has a limit-cycle attractor. Offset-boosting control phenomena in the system are also studied with different orders and parameters.

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“…Fractional integral and derivative operators have evolved over time [22,23]. Some fractional numerical simulations can be seen in [24,25]. In their review article "Fractional calculus in the sky," [26] D. Baleanu and R. P. Agrwal, two esteemed professors, provide the most recent compact review of fractional calculus.…”

Section: Introductionmentioning

confidence: 99%

New Fractional Estimates of Simpson-Mercer Type for Twice Differentiable Mappings Pertaining to Mittag-Leffler Kernel

Butt

Rashid

Javed

et al. 2022

Journal of Function Spaces

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The main motivation of this study is to introduce a novel auxiliary result of Simpson’s formula by employing the Mercer scheme for twice differentiable functions involving the Atangana-Baleanu (AB) fractional integral operator concerned with the Mittag-Leffler as a nonsingular or nonlocal kernel. Thus, by employing Mercer’s convexity on twice differentiable mappings along with Hölder’s and power-mean inequalities, one can develop a variety of new Simpson’s error estimates. Lastly, some applications to q -digamma function and modified Bessel functions are presented. Furthermore, the graphical illustrations described the efficiency and applicability of the proposed technique with success. We make links between our findings and a number of well-known discoveries in the literature. It is hoped that the proposed methodology will provide a new venue in the numerical techniques for calculating the quadrature formulae.

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Numerical simulation of fractional-order dynamical systems in noisy environments

Cited by 27 publications

References 58 publications

Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel

Advanced shifted first-kind Chebyshev collocation approach for solving the nonlinear time-fractional partial integro-differential equation with a weakly singular kernel

On fractional-order symmetric oscillator with offset-boosting control

New Fractional Estimates of Simpson-Mercer Type for Twice Differentiable Mappings Pertaining to Mittag-Leffler Kernel

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