Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 9Citation - Scopus: 9A High-Accuracy Vieta-Fibonacci Collocation Scheme To Solve Linear Time-Fractional Telegraph Equations(Taylor & Francis Ltd, 2022) Sadri, Khadijeh; Hosseini, Kamyar; Baleanu, Dumitru; Salahshour, SoheilThe vital target of the current work is to construct two-variable Vieta-Fibonacci polynomials which are coupled with a matrix collocation method to solve the time-fractional telegraph equations. The emerged fractional derivative operators in these equations are in the Caputo sense. Telegraph equations arise in the fields of thermodynamics, hydrology, signal analysis, and diffusion process of chemicals. The orthogonality of derivatives of shifted Vieta-Fibonacci polynomials is proved. A bound of the approximation error is ascertained in a Vieta-Fibonacci-weighted Sobolev space that admits increasing the number of terms of the series solution leads to the decrease of the approximation error. The proposed scheme is implemented on four illustrated examples and obtained numerical results are compared with those reported in some existing research works.Article Citation - WoS: 29Citation - Scopus: 21A New Fractional Infectious Disease Model Under the Non-Singular Mittag-Leffler Derivative(Taylor & Francis Ltd, 2022) Liu, Xuan; Ur Rahmamn, Mati; Ahmad, Saeed; Baleanu, Dumitru; Nadeem Anjam, YasirIn this manuscript, we consider a fractional mathematical model, which describes the dynamics of infectious disease, under the non-singular Mittag-Leffler derivative. The model under consideration is the extension of the SIRV model, where the infectious class has been divided into two compartments, namely the acute and chronically infectious individuals. First, we obtain the possible equilibrium states of the given model. With the help of the next generation matrix approach, the reproduction number has been calculated for the system to find conditions on the spread or control of the disease. Additionally, a new concept of strength number and analysis of the second derivative of the Lyapunov function has been used for the detection of waves. We investigate the said problem for qualitative analysis and determine at least one solution by applying the approach of fixed point theory. For approximate solution, the technique of iterative fractional-order Adams-Bashforth scheme has been used. Numerical simulation for the proposed scheme has been performed at various fractional-order lying between 0, 1 and for integer-order 1. All the compartments show convergency and stability with growing time. A good comparative result has been given by different fractional orders and achieves stability faster at the low fractional orders.Article Citation - WoS: 1Citation - Scopus: 1Scattering of Plane-Waves by an Impedance Half-Plane at the Interface Between Isorefractive Media(Taylor and Francis Ltd., 2018) Basdemir, Husnu DenizThe scattering of plane waves by an impedance half-plane located at the interface of two isorefractive media is investigated. The scattered field, in addition to the diffracted and geometrical optics fields, is analyzed numerically and compared to the scattered field of perfectly conducting half-plane. The effect of the isorefractive media on the scattered field is also examined. © 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group.