Matematik Bölümü

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Analyzing Transient Response of the Parallel Rcl Circuit By Using the Caputo–Fabrizio Fractional Derivative
(Springer, 2020) Baleanu, Dumitru; Baleanu, Dumitru; Rezapour, Shahram; 56389
In this paper, the transient response of the parallel RCL circuit with Caputo–Fabrizio derivative is solved by Laplace transforms. Also, the graphs of the obtained solutions for the different orders of the fractional derivatives are compared with each other and with the usual solutions. Finally, they are compared with practical and laboratory results.
Dağılım fonksiyonlarının yinelenmis fonksiyon sistemleri ile tahmini
(2014) Çilingir, Figen; 18416
Bir dağılım fonksiyonunun parametrik olmayan tahmin edicisi yinelenmis fonksiyon sistemleri kullanılarak elde edilebilmektedir. Bu yönteme göre, bir dağılım fonksiyonunun tahmin edicisi, (X1, X2,…,Xn) örneklemine bağlı olan bir p parametre vektörü ve w afin dönüsümleri ailesine göre tanımlanan T daralma operatörünün bir sabit noktası olarak düsünülmektedir. Döviz kuru verisi üzerinde yapılan uygulamadan elde edilen sonuçlar bir örnek olarak gösterilmistir.
Exact Solution of Two-Dimensional Fractional Partial Differential Equations
(2020) Baleanu, Dumitru; Jassim, Hassan Kamil; 56389
In this study, we examine adapting and using the Sumudu decomposition method (SDM) as a way to find approximate solutions to two-dimensional fractional partial differential equations and propose a numerical algorithm for solving fractional Riccati equation. This method is a combination of the Sumudu transform method and decomposition method. The fractional derivative is described in the Caputo sense. The results obtained show that the approach is easy to implement and accurate when applied to various fractional differential equations.
Explicit iteration to a nonlinear fractional Langevin equation with non-separated integro-differential strip-multi-point boundary conditions
(2020) Baleanu, Dumitru; Qin, Jianfang; Zhang, Lihong; Baleanu, Dumitru; 56389
By using the monotone iterative method combined with the upper and lower solutions, we not only prove the existence of extremal solutions for the nonlinear fractional Langevin equation involving fractional conformable derivative and non-separated integro-differential strip-multi-point boundary conditions, but also provide two computable explicit monotone iterative sequences that converge to the extremal solution. In order to carry out our work smoothly, we also develop a comparison principle, which plays a very important role in this article. (C) 2019 Elsevier Ltd. All rights reserved.

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