WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 47Citation - Scopus: 52A Delayed Plant Disease Model With Caputo Fractional Derivatives(Springer, 2022) Baleanu, Dumitru; Erturk, Vedat Suat; Inc, Mustafa; Govindaraj, V; Kumar, PushpendraWe analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams-Bashforth-Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study.Article Citation - WoS: 37Citation - Scopus: 43Stable Numerical Results To a Class of Time-Space Fractional Partial Differential Equations Via Spectral Method(Elsevier, 2020) Abdeljawad, Thabet; Shah, Kamal; Jarad, FahdIn 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.Article Citation - WoS: 217Citation - Scopus: 229Some Existence Results on Nonlinear Fractional Differential Equations(Royal Soc, 2013) Rezapour, Shahram; Mohammadi, Hakimeh; Baleanu, DumitruIn this paper, by using fixed-point methods, we study the existence and uniqueness of a solution for the nonlinear fractional differential equation boundary-value problem D(alpha)u(t) = f(t, u(t)) with a Riemann-Liouville fractional derivative via the different boundary-value problems u(0) = u(T), and the three-point boundary condition u(0)= beta(1)u(eta) and u(T) = beta(2)u(eta), where T > 0, t is an element of I = [0, T], 0 < alpha < 1, 0 < eta < T, 0 < beta(1) < beta(2) < 1.