Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Rezapour, ShahramPublisher: search.filters.publisher.Pergamon-elsevier Science Ltd

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  • Article
    Citation - WoS: 103
    Citation - Scopus: 107
    Some Novel Mathematical Analysis on the Fractal-Fractional Model of the Ah1n1/09 Virus and Its Generalized Caputo-Type Version
    (Pergamon-elsevier Science Ltd, 2022) Avci, Ibrahim; Kumar, Pushpendra; Baleanu, Dumitru; Rezapour, Shahram; Etemad, Sina
    In this paper, we formulate a new model of a particular type of influenza virus called AH1N1/09 in the framework of the four classes consisting of susceptible, exposed, infectious and recovered people. For the first time, we here investigate this model with the help of the advanced operators entitled the fractal-fractional operators with two fractal and fractional orders via the power law type kernels. The existence of solution for the mentioned fractal-fractional model of AH1N1/09 is studied by some special mappings such as ?-psi-contractions and ?-admissibles. The Leray-Schauder theorem is also applied for this aim. After investigating the stability criteria in four versions, to approximate the desired numerical solutions, we implement Adams-Bashforth (AB) scheme and simulate the graphs for different data on the fractal and fractional orders. Lastly, we convert our fractal-fractional AH1N1/09 model into a fractional model via the generalized Liouville-Caputo-type (GLC-type) operators and then, we simulate new graphs caused by the new numerical scheme called Kumar-Erturk method.
  • Article
    Citation - WoS: 716
    Citation - Scopus: 762
    A New Study on the Mathematical Modelling of Human Liver With Caputo-Fabrizio Fractional Derivative
    (Pergamon-elsevier Science Ltd, 2020) Jajarmi, Amin; Mohammadi, Hakimeh; Rezapour, Shahram; Baleanu, Dumitru
    In this research, we aim to propose a new fractional model for human liver involving Caputo-Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard-Lindelof approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives. (C) 2020 Elsevier Ltd. All rights reserved.