Browsing by Author "Kumar, Pushpendra"

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    A new fractional-order model for defining the dynamics of ending student strikes at a university
    (Springer int Publ Ag, 2024) Kumar, Pushpendra
    Nowadays, different real-life phenomena are being modelled using fractional-order operators. In this paper, a Caputo-type fractional-order mathematical model is proposed for defining the dynamics of ending student strikes at a university by taking per-year constant admissions. We analyse the possible strategies to control the strikes on the university campus. We prove the existence of a unique global solution for the given fractional-order model using a new characteristic of the well-known Mittag-Leffler function and fixed-point theory. We derive the numerical solution of the proposed model via the Haar wavelet method, which is one of the efficient numerical algorithms. A number of plots are performed, taking different cases, for a good understanding of the proposed problem. The aim of this study is to understand how fractional derivatives are useful to capture memory effects in such problems. All results are given with supporting arguments.
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    A Nonlinear Mathematical Model To Describe the Transmission Dynamics of the Citrus Canker Epidemic
    (Accscience Publishing, 2025) Kumar, Pushpendra
    In this article, a mathematical model is proposed to define the transmission dynamics of one of the most dangerous plant diseases, citrus canker, by using integer and fractional derivatives. For the fractional-order generalisation, the well-known Caputo fractional derivative is used with the singular-type kernel. The basic features of the proposed integer-and fractional-order models are defined by using well-known mathematical concepts. The proposed model is numerically solved by using the Chebyshev spectral collocation scheme. Some graphical justifications are also given to visualise the disease transmission in the population of citrus plants over time. This research study contains the first non-linear mathematical model of citrus canker transmission, which is the main novelty of this article.