Yazar "Ahmad, Hijaz" seçeneğine göre listele

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    A detailed study on a solvable system related to the linear fractional difference equation
    (Amer Inst Mathematical Sciences-Aims, 2021) Tollu, Durhasan Turgut; Yalcinkaya, Ibrahim; Ahmad, Hijaz; Yao, Shao-Wen
    In this paper, we present a detailed study of the following system of difference equations x(n+1) = a/1+y(n)x(n-1), y(n+1) = b/1+x(n)y(n-1), n is an element of N-0, where the parameters a, b, and the initial values x(-1), x(0), y(-1), Y-0 are arbitrary real numbers such that x(n) and y(n) are defined. We mainly show by using a practical method that the general solution of the above system can be represented by characteristic zeros of the associated third-order linear equation. Also, we characterized the well-defined solutions of the system. Finally, we study long-term behavior of the well-defined solutions by using the obtained representation forms.
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    On a System of k-Difference Equations of Order Three
    (Hindawi Ltd, 2020) Yalcinkaya, Ibrahim; Ahmad, Hijaz; Tollu, Durhasan Turgut; Li, Yong-Min
    In this paper, we deal with the global behavior of the positive solutions of the system of k-difference equations u(n+1)((1)) = (alpha(1)u(n-1)((1))/beta(1) + alpha(1)(u(n-2)((2)))(r1)), u(n+1)((2)) = alpha(2)u(n-1)((2))/beta(2) + alpha(2)(u(n-2)((3)))(r2), ... , u(n+1)((k)) = alpha(k)u(n-1)((k))/beta(k) + alpha(k)(u(n-2)((1)))(rk), n is an element of N-0, where the initial conditions u(-l)((i)) (l = 0, 1, 2) are nonnegative real numbers and the parameters alpha(i), beta(i), gamma(i), and r(i) are positive real numbers for i = 1, 2, ... , k, by extending some results in the literature. By the end of the paper, we give three numerical examples to support our theoretical results related to the system with some restrictions on the parameters.
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    An orthotropic thermo-viscoelastic infinite medium with a cylindrical cavity of temperature dependent properties via MGT thermoelasticity
    (De Gruyter Poland Sp Z O O, 2022) Abouelregal, Ahmed E.; Ahmad, Hijaz; Yavuz, Mehmet; Nofal, Taher A.; Alsulami, M. D.
    The current work is devoted to introduce a novel thermoelastic heat conduction model where the Moore-Gibson-Thompson (MGT) equation describes the heat equation. The constructed model is characterized by allowing limited velocities of heat wave propagation within the material, consistent with physical phenomena. The Green-Naghdi Type III model is improved by introducing the delay factor into the modified Fourier law. Also, from the presented model, some other models of thermoelasticity can be derived at specific states. Based on the suggested model, an infinite orthotropic material with a cylindrical hole exposed to time-dependent temperature variation was studied. It has also been considered that the coefficient of thermal conductivity varies with temperature, unlike in many other cases where this value is considered constant. The viscoelastic material of the investigated medium was assumed to be of the Kelvin-Voigt type. The Laplace transform method provides general solutions to the studied field variables equations. The effects of viscosity and thermal variability parameters on these fields are discussed and graphically presented. In addition, the numerical results were presented in tables, and a comparison with previous models was made to ensure the accuracy of the results of the proposed model.
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    An orthotropic thermo-viscoelastic infinite medium with a cylindrical cavity of temperature dependent properties via MGT thermoelasticity
    (De Gruyter Poland Sp Z O O, 2022) Abouelregal, Ahmed E.; Ahmad, Hijaz; Yavuz, Mehmet; Nofal, Taher A.; Alsulami, M. D.
    The current work is devoted to introduce a novel thermoelastic heat conduction model where the Moore-Gibson-Thompson (MGT) equation describes the heat equation. The constructed model is characterized by allowing limited velocities of heat wave propagation within the material, consistent with physical phenomena. The Green-Naghdi Type III model is improved by introducing the delay factor into the modified Fourier law. Also, from the presented model, some other models of thermoelasticity can be derived at specific states. Based on the suggested model, an infinite orthotropic material with a cylindrical hole exposed to time-dependent temperature variation was studied. It has also been considered that the coefficient of thermal conductivity varies with temperature, unlike in many other cases where this value is considered constant. The viscoelastic material of the investigated medium was assumed to be of the Kelvin-Voigt type. The Laplace transform method provides general solutions to the studied field variables equations. The effects of viscosity and thermal variability parameters on these fields are discussed and graphically presented. In addition, the numerical results were presented in tables, and a comparison with previous models was made to ensure the accuracy of the results of the proposed model.
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    Qualitative behavior of a higher-order fuzzy difference equation
    (American Institute of Mathematical Sciences (AIMS), 2023) Yalçınkaya, İbrahim; Tollu, Durhasan Turgut; Khastan, Alireza; Ahmad, Hijaz; Botmart, Thongchai
    In this paper, we investigate the qualitative behavior of the fuzzy difference equation zn +1 = Azn-s/B + C Pi(s)(i=0) z(n-i) where n is an element of N-0 = N boolean OR{0},(z(n)) is a sequence of positive fuzzy numbers, A; B; C and the initial conditions z j; j = 0; 1, ..., s are positive fuzzy numbers and s is a positive integer. Moreover, two examples are given to verify the e ffectiveness of the results obtained.
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    Soliton solutions for time fractional ocean engineering models with Beta derivative
    (Elsevier, 2022) Yalcinkaya, Ibrahim; Ahmad, Hijaz; Tasbozan, Orkun; Kurt, Ali
    In this study, the authors obtained the soliton and periodic wave solutions for time fractional symmetric regularized long wave equation (SRLW) and Ostrovsky equation (OE) both arising as a model in ocean engineering. For this aim modified extended tanh-function (mETF) is used. While using this method, chain rule is employed to turn fractional nonlinear partial differential equation into the nonlinear or-dinary differential equation in integer order. Owing to the chain rule, there is no further requirement for any normalization or discretization. Beta derivative which involves fractional term is used in considered mathematical models. Obtaining the exact solutions of these equations is very important for knowing the wave behavior in ocean engineering models.(c) 2021 Shanghai Jiaotong University. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )