A fractional mathematical modeling of protectant and curative fungicide application

Kumar, Pushpendra; Ertürk, Vedat Suat; Govindaraj, V.; Kumar, Sunil

doi:10.1016/j.csfx.2022.100071

Cited by 10 publications

(4 citation statements)

References 31 publications

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“…The model (4) has been shown positive results whenever the value of ω is decreased gradually from 1. [18,29,41,22,23,25].…”

Section: Discussionmentioning

confidence: 99%

“…There are numerous approaches in ecology and epidemiology to investigating population and SIR models in the form of systems of ordinary and partial differential equations, difference equations, and fractional-order differential equations. Among them, fractional order differential equations are the most commonly studied because they include various effects and hereditary properties that are important for studying stability characteristics in dynamical and SIR models [18,29,41,22,23]. The phenomenon of fractional order is more realistic as it incorporates the concept of non-integer models, which has been omitted in classical theory.…”

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confidence: 99%

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Stability analysis of fractional order modelling of social media addiction

Malik

Deepika

2023

MFC

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<p style='text-indent:20px;'>In this article, we explored the fractional order mathematical modelling of social media addiction. For the fractional order model of social media addiction, the free equilibrium point <inline-formula><tex-math id="M1">\begin{document}$ E_{0} $\end{document}</tex-math></inline-formula>, endemic equilibrium point <inline-formula><tex-math id="M2">\begin{document}$ E_{*} $\end{document}</tex-math></inline-formula>, and basic reproduction number <inline-formula><tex-math id="M3">\begin{document}$ R_0 $\end{document}</tex-math></inline-formula> have been found. We discussed the stability analysis of the order model of social media addiction through the next generation matrix and fractional Routh-Hurwitz criterion. We also explained the fractional order mathematical modelling of social media addiction by applying a highly reliable and efficient scheme known as q-Homotopy Analysis Sumudu Transformation Method (q-HASTM). This technique q-HASTM is the hybrid scheme based on q-HAM and Sumudu transform technique. In the end, the numerical simulation of the fractional order model of social media addiction is also explained by using the generalized Adams-Bashforth-Moulton method.</p>

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“…The model (4) has been shown positive results whenever the value of ω is decreased gradually from 1. [18,29,41,22,23,25].…”

Section: Discussionmentioning

confidence: 99%

mentioning

confidence: 99%

Stability analysis of fractional order modelling of social media addiction

Malik

Deepika

2023

MFC

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“…Rashid et al [11] explored childhood diseases and their complications via an SIR model involving the Atangana-Baleanu fractional derivative. In [12], a study on the dynamics of fungicide application was proposed via a fractional mathematical model with the Caputo-Fabrizio operator. In [13], Lauria et al established a novel intra-hour photovoltaic power forecasting method based on the Caputo-type fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

On Numerical Simulations of Variable-Order Fractional Cable Equation Arising in Neuronal Dynamics

Salama

2024

Fractal Fract

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In recent years, various complex systems and real-world phenomena have been shown to include memory and hereditary properties that change with respect to time, space, or other variables. Consequently, fractional partial differential equations containing variable-order fractional operators have been extensively resorted for modeling such phenomena accurately. In this paper, we consider the two-dimensional fractional cable equation with the Caputo variable-order fractional derivative in the time direction, which is preferable for describing neuronal dynamics in biological systems. A point-wise scheme, namely, the Crank–Nicolson finite difference method, along with a group-wise scheme referred to as the explicit decoupled group method are proposed to solve the problem under consideration. The stability and convergence analyses of the numerical schemes are provided with complete details. To demonstrate the validity of the proposed methods, numerical simulations with results represented in tabular and graphical forms are given. A quantitative analysis based on the CPU timing, iteration counting, and maximum absolute error indicates that the explicit decoupled group method is more efficient than the Crank–Nicolson finite difference scheme for solving the variable-order fractional equation.

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“…A proposed study on the role of natural microbial biostimulants to increase plant performance and protecting them against mosaic infection has been conducted using fractional nonlinear models (Kumar et al , 2021a). More recent research on fractional models arise in health sciences can be viewed in (Kumar et al , 2021b; Manickam et al , 2022; Kumar et al , 2022).…”

Section: Introductionmentioning

confidence: 99%

Solution of a nonlinear fractional COVID-19 model

Abukhaled

Khuri

Rabah

2022

HFF

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Purpose The purpose of this study is to obtain an analytical solution for a nonlinear system of the COVID-19 model for susceptible, exposed, infected, isolated and recovered. Design/methodology/approach The Laplace decomposition method and the differential transformation method are used. Findings The obtained analytical results are useful on two fronts: first, they would contribute to a better understanding of the dynamic spread of the COVID-19 disease and help prepare effective measures for prevention and control. Second, researchers would benefit from these results in modifying the model to study the effect of other parameters such as partial closure, awareness and vaccination of isolated groups on controlling the pandemic. Originality/value The approach presented is novel in its implementation of the nonlinear system of the COVID-19 model

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A fractional mathematical modeling of protectant and curative fungicide application

Cited by 10 publications

References 31 publications

Stability analysis of fractional order modelling of social media addiction

Stability analysis of fractional order modelling of social media addiction

On Numerical Simulations of Variable-Order Fractional Cable Equation Arising in Neuronal Dynamics

Solution of a nonlinear fractional COVID-19 model

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