Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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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, ThabetMiddle 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: 10Citation - Scopus: 11Chaotic Attractors and Fixed Point Methods in Piecewise Fractional Derivatives and Multi-Term Fractional Delay Differential Equations(Elsevier, 2023) Jarad, Fahd; Panda, Sumati Kumari; Abdeljawad, ThabetUsing generalized cyclic contractions, we establish some fixed point results in controlled rectangular metric spaces. Some subsequent outcomes are obtained. Moreover, some necessary conditions to demonstrate the existence of solutions for the multi-term fractional delay differential equations with wth order and the piecewise equations under the setting of non-singular type derivative are established in this paper. In order to demonstrate the effectiveness of our results, we provided some numerical examples.Article Citation - WoS: 98Citation - Scopus: 111On a Nonlinear Fractional Order Model of Dengue Fever Disease Under Caputo-Fabrizio Derivative(Elsevier, 2020) Shah, Kamal; Jarad, Fahd; Abdeljawad, ThabetIn this manuscript, we investigate epidemic model of dengue fever disease under Caputo and Fabrizio fractional derivative abbreviated as (CFFD). The respective investigation is devoted to qualitative theory of existence of solution for the model under consideration by using fixed point theory. After the establishing the qualitative aspect, we apply Laplace transform coupled with Ado-mian decomposition method to develop an algorithm for semi analytical solution under CFFD. In same line, we also develop the semi analytical solution for the considered model under usual Caputo fractional derivative (CFD). By using Matlab, we present both type of solutions via graphs and hence give some comparative remarks about the nature of the solutions of both derivatives. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).Article Citation - WoS: 26Citation - Scopus: 32On a More General Fractional Integration by Parts Formulae and Applications(Elsevier, 2019) Gomez-Aguilar, J. F.; Jarad, Fahd; Abdeljawad, Thabet; Atangana, AbdonThe integration by part comes from the product rule of classical differentiation and integration. The concept was adapted in fractional differential and integration and has several applications in control theory. However, the formulation in fractional calculus is the classical integral of a fractional derivative of a product of a fractional derivative of a given function f and a function g. We argue that, this formulation could be done using only fractional operators: thus, we develop fractional integration by parts for fractional integrals, Riemann-Liouville, Liouville-Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. We allow the left and right fractional integrals of order alpha > 0 to act on the integrated terms instead of the usual integral and then make use of the fractional type Leibniz rules to formulate the integration by parts by means of new generalized type fractional operators with binomial coefficients defined for analytic functions. In the case alpha = 1, our formulae of fractional integration by parts results in previously obtained integration by parts in fractional calculus. The two disciplines or branches of mathematics are built differently, while classical differentiation is built with the concept of rate of change of a given function, a fractional differential operator is a convolution. (C) 2019 Elsevier B.V. All rights reserved.Article Citation - WoS: 68Citation - Scopus: 81Efficient Sustainable Algorithm for Numerical Solutions of Systems of Fractional Order Differential Equations by Haar Wavelet Collocation Method(Elsevier, 2020) Shah, Kamal; Al-Mdallal, Qasem; Jarad, Fahd; Abdeljawad, Thabet; Amin, RohulThis manuscript deals a numerical technique based on Haar wavelet collocation which is developed for the approximate solution of some systems of linear and nonlinear fractional order differential equations (FODEs). Based on these techniques, we find the numerical solution to var-ious systems of FODEs. We compare the obtain solution with the exact solution of the considered problems at integer orders. Also, we compute the maximum absolute error to demonstrate the effi-ciency and accuracy of the proposed method. For the illustration of our results we provide four test examples. The experimental rates of convergence for different number of collocation point is calculated which is approximately equal to 2. Fractional derivative is defined in the Caputo sense. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).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: 47Citation - Scopus: 53Analysis of Some Generalized Abc - Fractional Logistic Models(Elsevier, 2020) Al-Mdallal, Qasem M.; Jarad, Fahd; Abdeljawad, Thabet; Hajji, Mohamed A.In this article, some logistic models in the settings of Caputo fractional operators with multi-parametered Mittag-Leffler kernels (ABC) are studied. This study mainly focuses on modified quadratic and cubic logistic models in the presence of a Caputo type fractional derivative. Existence and uniqueness theorems are proved and stability analysis is discussed by perturbing the equilib-rium points. Numerical illustrative examples are discussed for the studied models. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).Article Citation - WoS: 16Citation - Scopus: 17Fixed Point Theory for Generalized Contractions in Cone Metric Spaces(Elsevier, 2012) Amini-Harandi, A.; Baleanu, D.; Farajzadeh, A. P.; Turkoglu, Duran; Abuloha, Muhib; Abdeljawad, ThabetIn this paper, we prove some fixed point theorems for generalized contractions in cone metric spaces. Our theorems extend some results of Suzuki (2008) [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc Amer Math Soc 136(5) (2008), 1861-1869] and Kikkawa and Suzuki (2008) [M. Kikkawa and T. Suzuki, Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear Anal 69(9) (2008), 2942-2949]. (C) 2011 Elsevier B.V. All rights reserved.Article Citation - WoS: 120Citation - Scopus: 127Caputo Q-Fractional Initial Value Problems and a Q-Analogue Mittag-Leffler Function(Elsevier, 2011) Abdeljawad, Thabet; Baleanu, DumitruCaputo q-fractional derivatives are introduced and studied. A Caputo -type q-fractional initial value problem is solved and its solution is expressed by means of a new introduced q-Mittag-Leffler function. Some open problems about q-fractional integrals are proposed as well. (C) 2011 Elsevier B.V. All rights reserved.