Yazar "Cakmak, Musa" seçeneğine göre listele

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    Fibonacci collocation method for solving a class of nonlinear pantograph differential equations
    (Wiley, 2022) Cakmak, Musa
    In this study, a collocation method based on Fibonacci polynomials is used for approximately solving a class of nonlinear pantograph differential equations with initial and boundary conditions. The problem is first reduced into a nonlinear algebraic system via collocation points, later the unknown coefficients of the approximate solution function are calculated. Also, some problems are presented to test the performance of the proposed method by using the absolute error functions. Additionally, the obtained numerical results are compared with exact solutions of the test problems and approximate ones obtained with other methods in literature.
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    A Matrix Method Based on the Fibonacci Polynomials to the Generalized Pantograph Equations with Functional Arguments
    (Hindawi Ltd, 2014) Koc, Ayse Betul; Cakmak, Musa; Kurnaz, Aydin
    A pseudospectral method based on the Fibonacci operational matrix is proposed to solve generalized pantograph equations with linear functional arguments. By using this method, approximate solutions of the problems are easily obtained in form of the truncated Fibonacci series. Some illustrative examples are given to verify the efficiency and effectiveness of the proposed method. Then, the numerical results are compared with other methods.
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    A new Fibonacci type collocation procedure for boundary value problems
    (Springeropen, 2013) Koc, Ayse Betul; Cakmak, Musa; Kurnaz, Aydin; Uslu, Kemal
    In this study, we present a new procedure for the numerical solution of boundary value problems. This approach is mainly founded on the Fibonacci polynomial expansions, the so-called pseudospectral methods with the collocation method. The applicability and effectiveness of our proposed approach is shown by some illustrative examples. Then, the results indicate that this method is very effective and highly promising for linear differential equations defined on any subinterval of the real domain. MSC: 35A25.
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    A numerical method for solving a class of systems of nonlinear Pantograph differential equations
    (Elsevier, 2022) Cakmak, Musa; Alkan, Sertan
    In this paper, Fibonacci collocation method is firstly used for approximately solving a class of systems of nonlinear Pantograph differential equations with initial conditions. The problem is firstly reduced into a nonlinear algebraic system via collocation points, later the unknown coefficients of the approximate solution function are calculated. Also, some problems are presented to test the performance of the proposed method by using the absolute error functions. Additionally, the obtained numerical results are compared with exact solutions of the test problems and approximate ones obtained with other methods in the literature. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
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    Pell polynomial approach for solving a class of systems of nonlinear differential equations
    (Tbilisi Centre Math Sci, 2022) Cakmak, Musa; Alkan, Sertan
    In this study, Pell polynomial approach is used for approximately solving a class of systems of nonlinear differential equations with initial conditions. The given problem is firstly expressed as a matrix-vector system via collocation points. Then the unknown coefficients of the approximate solution are obtained. Also, some test problems are given to demonstrate accuracy and effectiveness of the proposed method. Additionally, the calculated numerical values are compared with exact solutions of the test problems and approximate ones obtained with other methods in literature.
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    Refinements of bullen-type inequalities for s-convex functions via Riemann-Liouville fractional integrals involving Gauss hypergeometric function
    (Taru Publications, 2019) Cakmak, Musa
    In this paper, the author establishes a new identity for differentiable functions and obtain some new inequalities for differentiable functions based on s-convexity via Riemann-Liouville fractional integrals involving Gauss hypergeometric function.
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    SOME NEW INEQUALITIES FOR DIFFERENTIABLE h-CONVEX FUNCTIONS AND APPLICATIONS
    (Univ Miskolc Inst Math, 2021) Cakmak, Musa; Tunc, Mevlut; Acem, Aysegul
    In this paper, the authors established a new identity for differentiable functions, afterwards they obtained some new inequalities for functions whose first derivatives in absolute value at certain powers are h-convex by using the identity. Also they give some applications for special means for arbitrary positive numbers.