Analysis on Krasnoselskii’s fixed point theorem of fuzzy variable fractional differential equation for a novel coronavirus (COVID-19) model with singular operator

Verma, Pratibha; Kumar, Manoj; Shukla, Anand

doi:10.1142/s1793962321500343

Cited by 7 publications

(2 citation statements)

References 16 publications

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“…The dynamics of this type of transmission are described using a fractional order derivative by [27][28][29][30][31][32][33], fractional-order backstepping strategy by Veisi and Delavari [34], generalized fractional-order by Xu et al [35], hybrid stochastic fractional order by Sweilam et al [36], El-Borai and El-Nadi [37], Caputo-Fabrizio (CF) and Atangana-Baleanu models non-singular fractional derivatives by Panwar et al [38], Mohammad and Trounev [39], Peter et al [40], Verma and Kumar [41], Sintunavarat and Turab [42], Kolebaje et al [43], optimized fractional order by Alshomrani et al [44], Caputo-Fabrizio derivative by Baleanu et al [45], fractional Chebyshev polynomials by Hadid et al [46], fractal-fractional order by Algehyne and Ibrahim [47], fractional order with fuzzy theory by Verma and Kumar [48], fractional order derivative with Krasnoselskiiʼs fixed point theorem by Verma et al [49], the multifractional characteristics with time-dependent memory indexes by Jahanshahi et al [50], fractional derivative with Riesz wavelets simulation by Mohammad et al [51]. Padmapriya and Kaliyappan [52], Dong et al [53] discussed the model of fuzzy fractional differential systems for the epidemic.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact

Santra,

Mahapatra,

Basu

2024

Phys. Scr.

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This article presents an epidemic disease propagation mathematical model in fractional order. The epidemiological characteristics are presented based on the susceptible, exposed, unknown infected, known infected, hospitalized population and the population in the secure zone. Both the disease endemic equilibrium and the disease-free equilibrium's stability characteristics have been examined using the basic reproduction number. Variation of basic reproduction number based on the different sensitive parameters has been discussed. It has been disputed whether the fractional model provides a uniform, reliable solution. An analysis of the time history of unknown and known infected populations, hospitalized populations and recovered populations at different values of various sensitive parameters has been carried out. To support the key theoretical conclusions, some numerical simulations are completed using MATLAB. The impact of various populations on the propagation of the illness has also been investigated, as well as how specific state variables change over time for various fractional order values.

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Section: Introductionmentioning

confidence: 99%

Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact

Santra,

Mahapatra,

Basu

2024

Phys. Scr.

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“…We can model and examine real-world problems that include uncertainty and fractional order derivatives by utilizing fuzzy-fractional diferential equations (FFDEs). Oceanography [31], biological population model [32], COVID-19 model [33], heat equation [34], and Fisher's equation [35] are some areas that employ FFDEs. Te Caputo fractional derivative [36] is one of the more popular defnitions of the fractional derivative.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

Qayyum,

Ahmad,

Tahir

et al. 2023

International Journal of Intelligent Systems

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This paper contains modeling of a fuzzy-fractional financial chaotic model based on triangular fuzzy numbers (TFNs) to predict the idea that long-term dependency and uncertainty both have an impact on the financial market. For solution purposes, the He–Mohand algorithm is proposed where homotopy perturbation is hybrid with Mohand transform in a fuzzy-Caputo sense. In analysis, solutions and corresponding errors at upper and lower bounds are estimated. The obtained numerical results are displayed in tables to show the reliability and efficiency of the proposed methodology. Upper bound errors range from 10 − 6 to 10 − 12 and lower bound errors from 10 − 6 to 10 − 11 . For graphical analysis, system profiles are illustrated as two-dimensional and three-dimensional plots at diverse values of fractional parameters and time to comprehend the physical behavior of the proposed fuzzy-fractional model. These plots demonstrate that the interest rate, price index, and investment demand decrease with the increase of the value of the r -cut at the lower bound. At the upper bound, this behavior is totally opposite. The chaotic behavior of the system at smaller values of saving rate, elasticity of demands, and per-investment cost is greater in contrast to their larger value. Analysis reveals that the proposed methodology (He–Mohand algorithm) provides a new way of understanding the complicated structure of financial systems and provides new insights into the dynamics of financial markets. This algorithm has potential applications in risk management, portfolio optimization, and trading strategies.

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Theoretical and Numerical Analysis of Fractional Order Mathematical Model on Recent COVID-19 Model Using Singular Kernel

Verma

Tiwari

Verma

2023

Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.

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This study presents a fractional-order mathematical model of coronavirus. We select COVID-19 model and convert the model into fractional order. Discuss its theoretical and numerical analysis. Firstly, we investigate the existence and uniqueness results using some fixed point theorems for the proposed fractional-order COVID-19 model. Further, we provide the stability analysis with the help of the Hyers-Ulam stability. The fractional operator is used in the Caputo sense. We obtain numerical solutions using famous numerical methods and provide a graphical interpretation using adopted numerical methods. Finally, we compare the above techniques and provide observations according to the obtained solutions.

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Analysis on Krasnoselskii’s fixed point theorem of fuzzy variable fractional differential equation for a novel coronavirus (COVID-19) model with singular operator

Cited by 7 publications

References 16 publications

Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact

Stability analysis of fractional epidemic model for two infected classes incorporating hospitalization impact

Modeling and Analysis of the Fuzzy-Fractional Chaotic Financial System Using the Extended He–Mohand Algorithm in a Fuzzy-Caputo Sense

Theoretical and Numerical Analysis of Fractional Order Mathematical Model on Recent COVID-19 Model Using Singular Kernel

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