Browsing by Author "Baleanu, Dumitru I."

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Citation - Scopus: 6
COVID-19 Classification Using Hybrid Deep Learning and Standard Feature Extraction Techniques
(Institute of Advanced Engineering and Science, 2023) El Shenbary, H. A.; Ebeid, Ebeid Ali; Baleanu, Dumitru I.; 01. Çankaya Üniversitesi; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi
There is no doubt that COVID-19 disease rapidly spread all over the world, and effected the daily lives of all of the people. Nowadays, the reverse transcription polymerase chain reaction is the most way used to detect COVID-19 infection. Due to time consumed in this method and material limitation in the hospitals, there is a need for developing a robust decision support system depending on artificial intelligence (AI) techniques to recognize the infection at an early stage from a medical images. The main contribution in this research is to develop a robust hybrid feature extraction method for recognizing the COVID-19 infection. Firstly, we train the Alexnet on the images database and extract the first feature matrix. Then we used discrete wavelet transform (DWT) and principal component analysis (PCA) to extract the second feature matrix from the same images. After that, the desired feature matrices were merged. Finally, support vector machine (SVM) was used to classify the images. Training, validating, and testing of the proposed method were performed. Experimental results gave (97.6%, 98.5%) average accuracy rate on both chest X-ray and computed tomography (CT) images databases. The proposed hybrid method outperform a lot of standard methods and deep learning neural networks like Alexnet, Googlenet and other related methods. © 2022 Elsevier B.V., All rights reserved.
Citation - WoS: 23
Citation - Scopus: 32
Duality of Singular Linear Systems of Fractional Nabla Difference Equations
(Elsevier Science inc, 2015) Baleanu, Dumitru I.; Dassios, Ioannis K.; 01. Çankaya Üniversitesi; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi
The main objective of this article is to provide a link between the solutions of an initial value problem of a linear singular system of fractional nabla difference equations, its proper dual system and its transposed dual system. By taking into consideration the case that the coefficients are square constant matrices with the leading coefficient singular, we study the prime system and by using the invariants of its pencil we give necessary and sufficient conditions for existence and uniqueness of solutions. After we prove that by using the pencil of the prime system we can study the existence and uniqueness of solutions of the proper dual system and the transposed dual system. Moreover their solutions, when they exist, can be explicitly represented without resorting to further processes of computations for each one separately. Finally, numerical examples are given based on a singular fractional nabla real dynamical system to justify our theory. (C) 2014 Elsevier Inc. All rights reserved.
Citation - WoS: 19
Citation - Scopus: 35
On a Singular System of Fractional Nabla Difference Equations With Boundary Conditions
(Springeropen, 2013) Baleanu, Dumitru I.; Dassios, Ioannis K.; 56389; 01. Çankaya Üniversitesi; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi
In this article, we study a boundary value problem of a class of linear singular systems of fractional nabla difference equations whose coefficients are constant matrices. By taking into consideration the cases that the matrices are square with the leading coefficient matrix singular, square with an identically zero matrix pencil and non-square, we provide necessary and sufficient conditions for the existence and uniqueness of solutions. More analytically, we study the conditions under which the boundary value problem has a unique solution, infinite solutions and no solutions. Furthermore, we provide a formula for the case of the unique solution. Finally, numerical examples are given to justify our theory.
Citation - WoS: 29
Citation - Scopus: 45
On Non-Homogeneous Singular Systems of Fractional Nabla Difference Equations
(Elsevier Science inc, 2014) Baleanu, Dumitru I.; Kalogeropoulos, Grigoris I.; Dassios, Ioannis K.; 56389; 01. Çankaya Üniversitesi; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi
In this article we study the initial value problem of a class of non-homogeneous singular systems of fractional nabla difference equations whose coefficients are constant matrices. By taking into consideration the cases that the matrices are square with the leading coefficient singular, non-square and square with a matrix pencil which has an identically zero determinant, we provide necessary and sufficient conditions for the existence and uniqueness of solutions. More analytically we study the conditions under which the system has unique, infinite and no solutions. Furthermore, we provide a formula for the case of the unique solution. Finally, numerical examples are given to justify our theory. Crown Copyright (C) 2013 Published by Elsevier Inc. All rights reserved.