Taylor Series Expansion Method To Compute Approximate Solution for Nonlinear Dynamical System

Huzaifa, Eiman; Khan, Adnan; Shah, Masaud; Khan, Mubashir Hayat

doi:10.48185/jfcns.v3i1.501

Cited by 3 publications

(2 citation statements)

References 18 publications

(18 reference statements)

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“…The most remarkable definitions in the fractional differential operators are mainly given by Riemann-Liouville, Caputo, Caputo-Fabrizio (CF) and Atangana-Baleanu in sense of Caputo (ABC), where, each operator has its characteristics. Detailed literature and motivated study related to fractional calculus have extensively been studied in [26][27][28][29]. Using fractional calculus techniques, one can represent the dynamics and memory of real-world phenomena which has a significant advantage because the fractional-order derivative is dependent not only on local conditions but also on history.…”

Section: Introductionmentioning

confidence: 99%

Chaotic dynamics in tritrophic interaction with volatile compounds in plants with power law kernel

Sami¹,

Saifullah²,

Ali³

et al. 2022

Phys. Scr.

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In this article, we study a fractional-order mathematical model representing tritrophic interaction amongst plants, herbivores, and carnivores with Caputo derivative. The existence and uniqueness of the system are investigated by fixed point theory, while the stability is studied by Hyers-Ulam and generalized Hyers-Ulam stability analysis. The Adams-Bashforth-Moulton scheme is used for numerical calculations. From numerical simulations, it is observed that when the fractional order decreases the system converges to a stable state. It is observed that for a small value of fractional order, the system approaches a stable state rapidly as compared to the integer order. The chaotic behavior of the system is studied using the Lyapunov spectrum. It is noted that two positive exponents of the proposed model show that the system is hyper-chaotic. It is also observed that a small value of attraction constant disrupts the system due to volatile organic compounds.

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Section: Introductionmentioning

confidence: 99%

Chaotic dynamics in tritrophic interaction with volatile compounds in plants with power law kernel

Sami¹,

Saifullah²,

Ali³

et al. 2022

Phys. Scr.

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“…Furthermore, a series of recent works has been proposed to model the dynamics of the COVID-19 virus using fractional derivatives [27][28][29] or the work of Huzaifa et al [30], which was used for another virus, the Ebola virus.…”

Section: Introductionmentioning

confidence: 99%

Prediction of COVID-19 Cases Using Constructed Features by Grammatical Evolution

Tsoulos

Tzallas²,

Tsalikakis³

2022

Symmetry

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A widely used method that constructs features with the incorporation of so-called grammatical evolution is proposed here to predict the COVID-19 cases as well as the mortality rate. The method creates new artificial features from the original ones using a genetic algorithm and is guided by BNF grammar. After the artificial features are generated, the original data set is modified based on these features, an artificial neural network is applied to the modified data, and the results are reported. From the comparative experiments done, it is clear that feature construction has an advantage over other machine-learning methods for predicting pandemic elements.

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Taylor Polynomial Enhancer using Genetic Programming for Symbolic Regression

Chang

Chiang

Hsu

et al. 2023

Proceedings of the Companion Conference on Genetic and Evolutionary Computation

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Taylor Series Expansion Method To Compute Approximate Solution for Nonlinear Dynamical System

Cited by 3 publications

References 18 publications

Chaotic dynamics in tritrophic interaction with volatile compounds in plants with power law kernel

Chaotic dynamics in tritrophic interaction with volatile compounds in plants with power law kernel

Prediction of COVID-19 Cases Using Constructed Features by Grammatical Evolution

Taylor Polynomial Enhancer using Genetic Programming for Symbolic Regression

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