On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

Shah, Kamal; Abdeljawad, Thabet; Jarad, Fahd; Al‐Mdallal, Qasem M.

doi:10.32604/cmes.2023.021523

Cited by 14 publications

(9 citation statements)

References 57 publications

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“…Their research highlighted the importance of the dynamics of epidemic infection rate and reproduction capacity. The significance and broad applicability of fractional models [ 11 ] and nonlinear dynamical systems through the differential transform [ 12 ]. In recent studies researchers have explored various aspects of fractional analysis in different contexts.…”

Section: Introductionmentioning

confidence: 99%

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

Nisar,

Farman,

Jamil

et al. 2024

PLoS ONE

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In this manuscript, we developed a nonlinear fractional order Ebola virus with a novel piecewise hybrid technique to observe the dynamical transmission having eight compartments. The existence and uniqueness of a solution of piecewise derivative is treated for a system with Arzel’a-Ascoli and Schauder conditions. We investigate the effects of classical and modified fractional calculus operators, specifically the classical Caputo piecewise operator, on the behavior of the model. A model shows that a completely continuous operator is uniformly continuous, and bounded according to the equilibrium points. The reproductive number R0 is derived for the biological feasibility of the model with sensitivity analysis with different parameters impact on the model. Sensitivity analysis is an essential tool for comprehending how various model parameters affect the spread of illness. Through a methodical manipulation of important parameters and an assessment of their impact on Ro, we are able to learn more about the resiliency and susceptibility of the model. Local stability is established with next Matignon method and global stability is conducted with the Lyapunov function for a feasible solution of the proposed model. In the end, a numerical solution is derived with Newton’s polynomial technique for a piecewise Caputo operator through simulations of the compartments at various fractional orders by using real data. Our findings highlight the importance of fractional operators in enhancing the accuracy of the model in capturing the intricate dynamics of the disease. This research contributes to a deeper understanding of Ebola virus dynamics and provides valuable insights for improving disease modeling and public health strategies.

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Section: Introductionmentioning

confidence: 99%

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

Nisar,

Farman,

Jamil

et al. 2024

PLoS ONE

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“…TDM includes nine unidentified parameters and is considered the highest accurate model due to its ability to address the effects of grain boundaries and leakage current coefficients 3 , 6 . Over the last few decades, estimating those parameters has been classified as a complex non-linear optimization problem 7 – 11 . This problem has been extensively tackled in the literature by either traditional techniques or approximation techniques 9 .…”

Section: Introductionmentioning

confidence: 99%

Novel hybrid kepler optimization algorithm for parameter estimation of photovoltaic modules

Mohamed,

Abdel-Basset,

Sallam

et al. 2024

Sci Rep

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The parameter identification problem of photovoltaic (PV) models is classified as a complex nonlinear optimization problem that cannot be accurately solved by traditional techniques. Therefore, metaheuristic algorithms have been recently used to solve this problem due to their potential to approximate the optimal solution for several complicated optimization problems. Despite that, the existing metaheuristic algorithms still suffer from sluggish convergence rates and stagnation in local optima when applied to tackle this problem. Therefore, this study presents a new parameter estimation technique, namely HKOA, based on integrating the recently published Kepler optimization algorithm (KOA) with the ranking-based update and exploitation improvement mechanisms to accurately estimate the unknown parameters of the third-, single-, and double-diode models. The former mechanism aims at promoting the KOA’s exploration operator to diminish getting stuck in local optima, while the latter mechanism is used to strengthen its exploitation operator to faster converge to the approximate solution. Both KOA and HKOA are validated using the RTC France solar cell and five PV modules, including Photowatt-PWP201, Ultra 85-P, Ultra 85-P, STP6-120/36, and STM6-40/36, to show their efficiency and stability. In addition, they are extensively compared to several optimization techniques to show their effectiveness. According to the experimental findings, HKOA is a strong alternative method for estimating the unknown parameters of PV models because it can yield substantially different and superior findings for the third-, single-, and double-diode models.

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“…There are many numerical methods proposed for solving PDE phenomena, for example, the finite volume method (FVM) [1], the finite different method (FDM) [2][3][4], the variational iteration method (VIM) [5][6][7][8]. There are also many works in numerical methods for solving PDE phenomena of all kinds; we mention some of them [9][10][11][12][13][14], and the homotopy perturbation method (HPM) [15][16][17][18][19][20][21][22][23][24][25][26]. This is the last one (HPM), which was established by He [5,27].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution of One-Dimensional Keller-Segel Equations via New Homotopy Perturbation Method

Slimani,

Lakhlifa,

Guesmia

2024

Contemp. Math.

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For solving a system of nonlinear partial differential equations (PDE) emerging in an attractor one-dimensional chemotaxis model, we used a relatively new analytical method called the new modified homotopy perturbation method (NMHPM). We use NMHPM for solving one-dimensional Keller-Segel models for different types. Some properties show biologically acceptable dependency on parameter values, and numerical solutions are provided. NMHPM’s stability and reduced computing time provide it with a broader range of applications. The algorithm provides analytical approximations for different types of Keller-Segel equations. Some numerical illustrations are given to show the efficiency of the algorithm.

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On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

Cited by 14 publications

References 57 publications

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

Computational and stability analysis of Ebola virus epidemic model with piecewise hybrid fractional operator

Novel hybrid kepler optimization algorithm for parameter estimation of photovoltaic modules

Analytical Solution of One-Dimensional Keller-Segel Equations via New Homotopy Perturbation Method

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