A numerical technique for variable-order fractional functional nonlinear dynamic systems

Keshi, Farzad Khane; Moghaddam, Behrouz Parsa; Aghili, Arman

doi:10.1007/s40435-019-00521-0

Cited by 7 publications

(2 citation statements)

References 37 publications

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“…reduces the duration of the constant. Artificial neural networks (INS) are being used successfully in many fields of science and technology due to their ability to help solve problems [16,17]. In addition to numerical solutions of semi-continuous differential equations, much research has been done to find solutions of exponential functions [18,19].…”

Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Adams-Bashforth-Moulton and Runge-Kutta Methods for Solving Ordinary Differential Equations Using MATLAB

Ali,

Abbas,

Abdelhakem

2024

MMEP

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This study deals with ordinary differential equations and their solutions consuming effective numerical methods. We observing for more accurate numerical methods proximate to MATLAB solutions. Approaches are Adams-Bashforth and Rung-Kutta-4 ought very good solutions, in the first response with ordinary differential equations of the primary order. Similarly, evaluation of modified second order numerical answers using, MATLAB and Adams-Bashfort-Moulton, by differential equation addition to numerical modeling methods expending fourth-order Runge-Kutta yielded excellent results. For the reason that the solutions are validated with high credibility, we explored in turn to best approximation results computed for the purpose of correcting them. Objective of new approach of this study was illustrated clear picture thru solving two examples with different numerical approximation methods. Compared are clearly shown in tables and figures to determine effectiveness and choose the best accuracy. We calculated different performance indices for several numerical methods using MATLAB and Moulton which yielded an excellent approximation through exams. We recommend it to be widely used in the future, and strive to develop it with faster and more accurate solutions.

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Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Adams-Bashforth-Moulton and Runge-Kutta Methods for Solving Ordinary Differential Equations Using MATLAB

Ali,

Abbas,

Abdelhakem

2024

MMEP

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“…Among the great variety of fractional differential equations used to model a wide range of complex physical processes (Keshi et al 2019;Alsuyuti et al 2019), multi-order fractional differential equations have gained a considerable interest due to their flexibility to describe complex multi-rate physical processes (Diethelm 2010). The aim of this paper is not to provide an exhaustive review of all developments with regard to spectral methods for fractional differential equations, rather, it aims to develop Legendre-Jacobi spectral collocation method to handle multi-order fractional initial value problems.…”

Section: Introductionmentioning

confidence: 99%

On the rate of convergence of spectral collocation methods for nonlinear multi-order fractional initial value problems

Zaky

Ameen

2019

Comp. Appl. Math.

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Multi-order fractional differential equations are motivated by their flexibility to describe complex multi-rate physical processes. This paper is concerned with the convergence behavior of a spectral collocation method when used to approximate solutions of nonlinear multi-order fractional initial value problems. The collocation scheme and its convergence analysis are developed based on the novel spectral collocation method which has been recently presented by Wang et al. (J Sci Comput 76(1):166-188, 2018) for single fractional-order boundary value problems. The proposed method is an indirect approach since we act on the equivalent Volterra integral equation of the second kind. More precisely, the spectral rate of convergence for the proposed method is established in the L 2 -and L ∞ -norms. The method enjoys high accuracy for problems with smooth solutions. Exponentially rapid convergence is observed with a small number of degree of freedoms and for all samples of fractional orders. Numerical examples are presented to support the theoretical finding.

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A comparative analysis of two algorithms for the simulation of fractional differential equations

Maamri

Trigeassou

2019

Int. J. Dynam. Control

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A numerical technique for variable-order fractional functional nonlinear dynamic systems

Cited by 7 publications

References 37 publications

Comparative Analysis of Adams-Bashforth-Moulton and Runge-Kutta Methods for Solving Ordinary Differential Equations Using MATLAB

Comparative Analysis of Adams-Bashforth-Moulton and Runge-Kutta Methods for Solving Ordinary Differential Equations Using MATLAB

On the rate of convergence of spectral collocation methods for nonlinear multi-order fractional initial value problems

A comparative analysis of two algorithms for the simulation of fractional differential equations

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