PubMed İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8650

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Author: search.filters.author.Shah, KamalPublisher: search.filters.publisher.Elsevier

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Now showing 1 - 3 of 3
  • Article
    Citation - WoS: 34
    Citation - Scopus: 43
    Study of Global Dynamics of Covid-19 Via a New Mathematical Model
    (Elsevier, 2020) Seadawy, Aly R.; Shah, Kamal; Ullah, Aman; Baleanu, Dumitru; Din, Rahim Ud
    The theme of this paper focuses on the mathematical modeling and transmission mechanism of the new Coronavirus shortly noted as (COVID-19), endangering the lives of people and causing a great menace to the world recently. We used a new type epidemic model composed on four compartments that is susceptible, exposed, infected and recovered (SEIR), which describes the dynamics of COVID-19 under convex incidence rate. We simulate the results by using nonstandard finite difference method (NSFDS) which is a powerful numerical tool. We describe the new model on some random data and then by the available data of a particular regions of Subcontinents.
  • Article
    Citation - WoS: 44
    Citation - Scopus: 53
    On a New Conceptual Mathematical Model Dealing the Current Novel Coronavirus-19 Infectious Disease
    (Elsevier, 2020) Shah, Kamal; Seadawy, Aly; Alrabaiah, Hussam; Baleanu, Dumitru; Din, Anwarud
    The present paper describes a three compartment mathematical model to study the transmission of the current infection due to the novel coronavirus (2019-nCoV or COVID-19). We investigate the aforesaid dynamical model by using Atangana, Baleanu and Caputo (ABC) derivative with arbitrary order. We derive some existence results together with stability of Hyers-Ulam type. Further for numerical simulations, we use Adams-Bashforth (AB) method with fractional differentiation. The mentioned method is a powerful tool to investigate nonlinear problems for their respective simulation. Some discussion and future remarks are also given.
  • Article
    Citation - WoS: 37
    Citation - Scopus: 43
    Stable Numerical Results To a Class of Time-Space Fractional Partial Differential Equations Via Spectral Method
    (Elsevier, 2020) Abdeljawad, Thabet; Shah, Kamal; Jarad, Fahd
    In this paper, we are concerned with finding numerical solutions to the class of time-space fractional partial differential equations: D(t)(p)u(t, x) + kappa D(x)(p)u(t, x) + tau u(t, x) = g(t, x), 1 < p < 2, (t, x) is an element of [0,1] x [0, 1], under the initial conditions. u(0, x) = theta(x), u(t)(0, x) = phi(x), and the mixed boundary conditions. u(t, 0) = u(x)(t, 0) = 0, where D-t(p) is the arbitrary derivative in Caputo sense of order p corresponding to the variable time t. Further, D-x(p) is the arbitrary derivative in Caputo sense with order p corresponding to the variable space x. Using shifted Jacobin polynomial basis and via some operational matrices of fractional order integration and differentiation, the considered problem is reduced to solve a system of linear equations. The used method doesn't need discretization. A test problem is presented in order to validate the method. Moreover, it is shown by some numerical tests that the suggested method is stable with respect to a small perturbation of the source data g(t, x). Further the exact and numerical solutions are compared via 3D graphs which shows that both the solutions coincides very well. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Cairo University.