Yazar "Yalcinkaya, Ibrahim" 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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    GLOBAL BEHAVIOR OF A THREE-DIMENSIONAL SYSTEM OF DIFFERENCE EQUATIONS OF ORDER THREE
    (Ankara Univ, Fac Sci, 2019) Tollu, Durhasan Turgut; Yalcinkaya, Ibrahim
    In this paper, we investigate the global behavior of the positive solutions of the system of difference equations u(n+1) = alpha(1)u(n-1)/beta(1)+gamma(1)v(n-2)(p) , v(n+1) = alpha(2)v(n-1)/beta(2)+gamma(2)w(n-2)(q) , w(n+1) = alpha(3)w(n-1)/beta(3)+gamma(3)u(n-2)(r) for n is an element of N-0 where the initial conditions u-i, v-i, w-i (i = 0, 1, 2) are non-negative real numbers and the parameters alpha(j), beta(j), gamma(j) (j = 1, 2, 3) and p, q, r are positive real numbers, by extending some results in the literature.
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    Global Stability of an Economic Model
    (Util Math Publ Inc, 2014) El-Metwally, H.; Yalcinkaya, Ibrahim; Cinar, Cengiz
    In this paper, we investigate the global stability of the following economic system of difference equations { x(n+1) = (1 - alpha)x(n) + beta x(n)(1 - x(n))e(-(xn+yn)) y(n+1) = (1 - alpha)y(n) + beta y(n)(1 - y(n))e(-(xn+yn)) , n = 0, 1, ... , (I) where alpha, and beta is an element of (0, infinity) with the initial conditions x(0) and y(0) is an element of (0,infinity). First we study the global behavior of the following general system of difference equations X-n((1)) = phi(1)(x(n-s1)((1))(1), x(n-s1)((2)(2))), X-n((2)) = phi(2)(x(n-s2)((2))(2), x(n-s1)((3)(3))), X-n((3)) = phi(3)(x(n-s2)((3))(3), x(n-s1)((4)(4))), X-n((k)) = phi(k)(x(n-s2)((k))(k), x(n-s2)((1)(1))). for n is an element of N-o where s(1)((i)), S-2((i)) is an element of N-o for i = 1,2, ... , k, with positive initial conditions. Second we apply the obtained results to investigate the global stability of System (I).
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    On a fuzzy difference equation
    (Util Math Publ Inc, 2014) Hatir, Esref; Mansour, Toufik; Yalcinkaya, Ibrahim
    In this paper, we investigate the existence, boundedness, asymptotic behavior and oscillatory behavior of the positive solutions of the fuzzy difference equation x(n+1) = A+B/x(n-1), n = 0, 1, 2, ..., where x(n) is a sequence of fuzzy numbers and A, B, x(0), and x(-1) are fuzzy numbers.
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    ON A NONLINEAR FUZZY DIFFERENCE EQUATION
    (Ankara Univ, Fac Sci, 2022) Yalcinkaya, Ibrahim; Caliskan, Vildan; Tollu, Durhasan Turgut
    In this paper we investigate the existence, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation z(n+1) = Az(n-1)/1 + Z(n-2)(p),n is an element of N-0 where (z(n)) is a sequence of positive fuzzy numbers, A and the initial conditions z(-j) (j = 0, 1,2) are positive fuzzy numbers and p is a positive integer.
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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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    ON THE DIFFERENCE EQUATION OF HIGHER ORDER
    (Util Math Publ Inc, 2013) Cinar, Cengiz; Mansour, Toufik; Yalcinkaya, Ibrahim
    In this paper, we investigate the global behavior of the difference equation [GRAPHICS] where k is a positive integer, a, alpha epsilon (0, infinity) and x(0),x(-1), ...x(-k) > 0.
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    On the dynamics of a higher-order fuzzy difference equation with rational terms
    (Springer, 2023) Yalcinkaya, Ibrahim; El-Metwally, Hamdy; Bayram, Mustafa; Tollu, Durhasan Turgut
    In this paper, we investigate existence, boundedness, asymptotic behavior and the oscillatory behavior of the positive solutions of the fuzzy difference equation z(n+1) = A + B/z(n-m1) + C/z(n-m2), n is an element of N-0, where (z(n)) is a sequence of positive fuzzy numbers, A, B, C and the initial values z(-j), j = 0, 1,..., s, are positive fuzzy numbers and m(1), m(2) are nonnegative integers with s = max {m(1), m(2)}. By studying this equation, we generalize and improve some results from the literature.
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    On the Max-Type Equation xn+1 = max{1/xn, Anxn-1} with a Period-Two Parameter
    (Hindawi Ltd, 2012) Yalcinkaya, Ibrahim
    We study the behavior of the well-defined solutions of the max type difference equation x(n+1) = max{1/x(n), A(n)x(n-1)}, n = 0, 1, . . . , where the initial conditions are arbitrary nonzero real numbers and {A(n)} is a period-two sequence of real numbers with A(n) is an element of [0,infinity).
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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/ )