Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
Permanent URI for this collectionhttps://hdl.handle.net/11147/7148
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Article A Chebyshev Wavelet Approach to the Generalized Time-Fractional Burgers-Fisher Equation(Univ Tabriz, 2025) Aghazadeh, Nasser; 01. Izmir Institute of Technology; 04. Faculty of Science; 04.02. Department of MathematicsThis work proposes a new method for obtaining the approximate solution of the time-fractional generalized BurgersFisher equation. The method's main idea is based on converting the nonlinear partial differential equation to a linear partial differential equation using the Picard iteration method. Then, the second kind Chebyshev wavelet collocation method is used to solve the linear equation obtained in the previous step. The technique is called the Chebyshev Wavelet Picard Method (CWPM). The proposed method successfully solves the time fractional generalized Burgers-Fisher equation. The obtained numerical results are compared with the exact solutions and with the solutions obtained using the Haar wavelet Picard method and the homotopy perturbation method.Article An Efficient Chebyshev Wavelet Collocation Technique for the Time-Fractional Camassa-Holm Equation(World Scientific Publ Co Pte Ltd, 2025) Aghazadeh, Nasser; Aghazadeh, Nasser; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyBy employing the third-order Chebyshev collocation technique along with relevant wavelets, we tackle a third-order singular fractional partial differential equation (PDE). We directly build the Chebyshev operation matrix of the third kind, avoiding the use of the block-pulse function or any approximations. To reduce the order of equation in this approach, we transform the higher-order PDEs into a system of PDEs. Next, we utilize the third-kind Chebyshev wavelet collocation method to convert the resulting system from the prior step into a set of algebraic equations. To demonstrate the method's effectiveness, we apply it to the time-fractional Camassa-Holm equation and a third-order time-singular PDE. The outcomes are compared with those from several established methods to illustrate the method's efficiency and practicality.Article Citation - WoS: 5Citation - Scopus: 6Lung Parenchyma Segmentation From Ct Images With a Fully Automatic Method(Springer, 2023) Mousavi Moghaddam, Reza; Aghazadeh, Nasser; Aghazadeh, Nasser; 04.02. Department of Mathematics; 04. Faculty of Science; 01. Izmir Institute of TechnologyFor the last three years, the world has been facing an infectious disease that primarily affects the human breathing organ. The disease has caused many deaths worldwide so far and has imposed high economic costs on all countries. Therefore, attention to computer-aided detection/diagnosis (CAD) systems to help diagnose and treat diseases related to the human respiratory system should be given more attention so that countries’ health systems can treat patients in epidemics. Considering the importance of CAD systems, we proposed a two-step automatic algorithm. In the first step, we obtain the primary boundary of the lobes in CT lung scan images with the help of some conventional image processing tools. In the second stage, we obtained a more precise boundary of the lung lobes by correcting the unusual dimples and valleys (which are sometimes caused by the presence of juxtapleural nodules). This proposed method has low implementation time. Given that a precise boundary of the pulmonary lobes is essential in the more accurate diagnosis of lung-related diseases, an attempt has been made to ensure that the final segmentation of the lung parenchyma has an acceptable score in terms of evaluation criteria so that the proposed algorithm can be used in the diagnosis procedure. © 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.