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Browsing by Author "Khan, H."

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    Erratum
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    Article
    A Fractional Order Covid-19 Epidemic Model With Mittag–leffler Kernel
    (Springer, 2023) Khan, H.; Ibrahim, M.; Khan, A.; Tunç, O.; Abdeljawad, T.
    We consider a nonlinear fractional-order Covid-19 model in a sense of the Atagana–Baleanu fractional derivative used for the analytic and computational studies. The model consists of six classes of persons, including susceptible, protected susceptible, asymptomatic infected, symptomatic infected, quarantined, and recovered individuals. The model is studied for the existence of solution with the help of a successive iterative technique with limit point as the solution of the model. The Hyers–Ulam stability is also studied. A numerical scheme is proposed and tested on the basis of the available literature. The graphical results predict the curtail of spread within the next 5000 days. Moreover, there is a gradual increase in the population of protected susceptible individuals. © 2023, Springer Nature Switzerland AG.
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    Article
    On System of Variable Order Nonlinear P-Laplacian Fractional Differential Equations With Biological Application
    (MDPI, 2023) Khan, H.; Alzabut, J.; Gulzar, H.; Tunç, O.; Pinelas, S.
    The study of variable order differential equations is important in science and engineering for a better representation and analysis of dynamical problems. In the literature, there are several fractional order operators involving variable orders. In this article, we construct a nonlinear variable order fractional differential system with a p-Laplacian operator. The presumed problem is a general class of the nonlinear equations of variable orders in the ABC sense of derivatives in combination with Caputo’s fractional derivative. We investigate the existence of solutions and the Hyers–Ulam stability of the considered equation. The presumed problem is a hybrid in nature and has a lot of applications. We have given its particular example as a waterborne disease model of variable order which is analysed for the numerical computations for different variable orders. The results obtained for the variable orders have an advantage over the constant orders in that the variable order simulations present the fluctuation of the real dynamics throughout our observations of the simulations. © 2023 by the authors.