https://hdl.handle.net/20.500.12809/8883 Fri, 10 Apr 2026 13:10:37 GMT 2026-04-10T13:10:37Z https://hdl.handle.net/20.500.12809/9498 A spectral collocation matrix method for solving linear Fredholm integro-differential–difference equations Öztürk, Yalçın; Demir, Atılım İlker In this study, a spectral collocation matrix method has been introduced to solve the linear Fredholm integro differential–difference equation (LFIDDE) numerically. The method is combined Chebyshev series and matrix algebras. As it is assumed that the truncated second-kind Chebyshev series is a solution of the given LFIDDEs, the matrix form of the each part of LFIDDEs is put into the LFIDDEs which is transformed a matrix-vector equation. The coefficients of the truncated second-kind Chebyshev series are obtained to solving such a linear equation. The given method’s quality and reliability are shown in some numerical examples and comparisons of some methods Fri, 01 Jan 2021 00:00:00 GMT https://hdl.handle.net/20.500.12809/9498 2021-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/9279 Numerical solution of fractional differential equations using fractional Chebyshev polynomials Öztürk, Yalçın; Ünal, Mutlu In this paper, fractional order Chebyshev polynomials are presented and some properties are given. Using definition of fractional order Chebyshev polynomials, we give a numerical scheme for solving fractional differential equation by the collocation method. The Collocation method converts the given fractional differential equation into a matrix equation, which yields a linear algebraic system. Bagley-Torvik equation and fractional relaxation-oscillation equation are solved to show the effectiveness of the given method. This method is compared with some known schemes Fri, 01 Jan 2021 00:00:00 GMT https://hdl.handle.net/20.500.12809/9279 2021-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/9215 An operational matrix method to solve linear Fredholm–Volterra integro‑differential equations with piecewise intervals Öztürk, Yalçın; Gülsu, Mustafa In recent times, operational matrix methods become overmuch popular. Actually, we have many more operational matrix methods. In this study, a new remodeled method is offered to solve linear Fredholm-Volterra integro-differential equations (FVIDEs) with piecewise intervals using Chebyshev operational matrix method. Using the properties of the Chebyshev polynomials, the Chebyshev operational matrix method is used to reduce FVIDEs into a linear algebraic equations. Some numerical examples are solved to show the accuracy and validity of the proposed method. Moreover, the numerical results are compared with some numerical algorithm. Fri, 01 Jan 2021 00:00:00 GMT https://hdl.handle.net/20.500.12809/9215 2021-01-01T00:00:00Z https://hdl.handle.net/20.500.12809/3920 A Collocation Method for Solving Fractional Riccati Differential Equation Öztürk, Yalçın; Anapalı, Ayşe; Gülsu, Mustafa; Sezer, Mehmet We have introduced a Taylor collocation method, which is based on collocation method for solving fractional Riccati differential equation with delay term. This method is based on first taking the truncated Taylor expansions of the solution function in the fractional Riccati differential equation and then substituting their matrix forms into the equation. Using collocation points, we have the system of nonlinear algebraic equation. Then, we solve the system of nonlinear algebraic equation using Maple 13, and we have the coefficients of the truncated Taylor sum. In addition, illustrative examples are presented to demonstrate the effectiveness of the proposed method. Comparing the methodology with some known techniques shows that the present approach is relatively easy and highly accurate. WOS: 000323971500001 Tue, 01 Jan 2013 00:00:00 GMT https://hdl.handle.net/20.500.12809/3920 2013-01-01T00:00:00Z