PubMed İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8650
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Browsing PubMed İndeksli Yayınlar Koleksiyonu by Author "Abdeljawad, Thabet"
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Article Citation - WoS: 35Citation - Scopus: 42Lyapunov-Type Inequalities for Mixed Non-Linear Forced Differential Equations Within Conformable Derivatives(Springer, 2018) Jarad, Fahd; Ozbekler, Abdullah; Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, Jehad; 234808; 114439; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiWe state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + r(1)(t)vertical bar X(t)vertical bar(eta-1) X(t) + r(2)(t)vertical bar x(t)vertical bar(delta-1) X(t) = g(t), t is an element of (a, b), satisfying the Dirichlet boundary conditions x(a) = x(b) = 0, where r(1), r(2), and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0 < eta < 1 < delta < 2. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative T-alpha(a) is replaced by a sequential conformable derivative T-alpha(a) circle T-alpha(a), alpha is an element of (1/2,1]. The potential functions r(1), r(2) as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.Article Citation - WoS: 6Citation - Scopus: 6Modeling the Transmission Dynamics of Middle Eastern Respiratory Syndrome Coronavirus with the Impact of Media Coverage(Elsevier, 2021) Fatima, BiBi; Alqudah, Manar A.; Zaman, Gul; Jarad, Fahd; Abdeljawad, Thabet; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiMiddle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R-0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.Article Citation - WoS: 85Qualitative Analysis of a Mathematical Model in the Time of Covid-19(Hindawi Ltd, 2020) Mahariq, Ibrahim; Jarad, Fahd; Shah, Kamal; Abdeljawad, Thabet; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiIn this article, a qualitative analysis of the mathematical model of novel corona virus named COVID-19 under nonsingular derivative of fractional order is considered. The concerned model is composed of two compartments, namely, healthy and infected. Under the new nonsingular derivative, we, first of all, establish some sufficient conditions for existence and uniqueness of solution to the model under consideration. Because of the dynamics of the phenomenon when described by a mathematical model, its existence must be guaranteed. Therefore, via using the classical fixed point theory, we establish the required results. Also, we present the results of stability of Ulam's type by using the tools of nonlinear analysis. For the semianalytical results, we extend the usual Laplace transform coupled with Adomian decomposition method to obtain the approximate solutions for the corresponding compartments of the considered model. Finally, in order to support our study, graphical interpretations are provided to illustrate the results by using some numerical values for the corresponding parameters of the model.Article Citation - WoS: 36Citation - Scopus: 42Stable Numerical Results To a Class of Time-Space Fractional Partial Differential Equations Via Spectral Method(Elsevier, 2020) Abdeljawad, Thabet; Shah, Kamal; Jarad, Fahd; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiIn 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: 36Citation - Scopus: 38Study of Impulsive Problems Under Mittag-Leffler Power Law(Elsevier Sci Ltd, 2020) Shah, Kamal; Jarad, Fahd; Abdo, Mohammed S.; Abdeljawad, Thabet; 234808; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya ÜniversitesiThis article is fundamentally concerned with deriving the solution formula, existence, and uniqueness of solutions of two types of Cauchy problems for impulsive fractional differential equations involving Atangana-Baleanu-Caputo (ABC) fractional derivative which possesses nonsingular Mittag-Leffler kernel. Our investigation is based on nonlinear functional analysis and some fixed point techniques. Besides, some examples are given delineated to illustrate the effectiveness of our outcome.
