Matematik Bölümü Yayın Koleksiyonu

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

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Author: search.filters.author.Kumar, DevendraSubject: search.filters.subject.Fixed Point Theorem

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 108
    Citation - Scopus: 122
    A New Analysis of Fractional Fish Farm Model Associated With Mittag-Leffler Kernel
    (World Scientific Publ Co Pte Ltd, 2020) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
    In this paper, we analyze the dynamical behavior of fish farm model related to Atangana-Baleanu derivative of arbitrary order. The model is constituted with the group of non-linear differential equations having nutrients, fish and mussel. We have included discrete kind gestational delay of fish. The solution of fish farm model is determined by employing homotopy analysis transforms method (HATM). Existence of and uniqueness of solution are studied through Picard-Lindelof approach. The influence of order of new non-integer order derivative on nutrients, fish and mussel is discussed. The complete study reveals that the outer food supplies manage the behavior of the model. Moreover, to show the outcomes of the study, some numerical results are demonstrated through graphs.
  • Article
    Citation - WoS: 158
    Citation - Scopus: 150
    A New Fractional Sirs-Si Malaria Disease Model With Application of Vaccines, Antimalarial Drugs, and Spraying
    (Springer, 2019) Singh, Jagdev; Al Qurashi, Maysaa; Baleanu, Dumitru; Kumar, Devendra
    The present paper deals with a new fractional SIRS-SI model describing the transmission of malaria disease. The SIRS-SI malaria model is modified by using the Caputo-Fabrizio fractional operator for the inclusion of memory. We also suggest the utilization of vaccines, antimalarial medicines, and spraying for the treatment and control of the malaria disease. The theory of fixed point is utilized to examine the existence of the solution of a fractional SIRS-SI model describing spreading of malaria. The uniqueness of the solution of SIRS-SI model for malaria is also analyzed. It is shown that the treatments have great impact on the dynamical system of human and mosquito populations. The numerical simulation of fractional SIRS-SI malaria model is performed with the aid of HATM and Maple packages to show the effect of different parameters of the treatment of malaria disease. The numerical results for fractional SIRS-SI malaria model reveal that the recommended approach is very accurate and effective.
  • Article
    Citation - WoS: 121
    Citation - Scopus: 142
    On the Analysis of Fractional Diabetes Model With Exponential Law
    (Springer, 2018) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
    In this work, we study the diabetes model and its complications with the Caputo-Fabrizio fractional derivative. A deterministic mathematical model pertaining to the fractional derivative of the diabetes mellitus is discussed. The analytical solution of the diabetes model is derived by exerting the homotopy analysis method, the Laplace transform and the Pade approximation. Moreover, existence and uniqueness of the solution are examined by making use of fixed point theory and the Picard-Lindelof approach. Ultimately, for illustrating the obtained results some numerical simulations are performed.