Matematik Bölümü Yayın Koleksiyonu

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

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Author: search.filters.author.Singh, JagdevPublisher: search.filters.publisher.Springer

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 122
    Citation - Scopus: 138
    A New Numerical Algorithm for Fractional Fitzhugh-Nagumo Equation Arising in Transmission of Nerve Impulses
    (Springer, 2018) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra
    The principal objective of this study is to present a new numerical scheme based on a combination of q-homotopy analysis approach and Laplace transform approach to examine the Fitzhugh-Nagumo (F-N) equation of fractional order. The F-N equation describes the transmission of nerve impulses. In order to handle the nonlinear terms, the homotopy polynomials are employed. To validate the results derived by employing the used scheme, we study the F-N equation of arbitrary order by using the fractional reduced differential transform scheme. The error analysis of the proposed approach is also discussed. The outcomes are shown through the graphs and tables that elucidate that the used schemes are very fantastic and accurate.
  • 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.
  • Article
    Citation - WoS: 119
    Citation - Scopus: 130
    A Hybrid Computational Approach for Klein-Gordon Equations on Cantor Sets
    (Springer, 2017) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra
    In this letter, we present a hybrid computational approach established on local fractional Sumudu transform method and homotopy perturbation technique to procure the solution of the Klein-Gordon equations on Cantor sets. Four examples are provided to show the accuracy and coherence of the proposed technique. The outcomes disclose that the present computational approach is very user friendly and efficient to compute the nondifferentiable solution of Klein-Gordon equation involving local fractional operator.