Matematik Bölümü

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Advanced Theoretical and Applied Studies of Fractional Differential Equations 2013
(Hindawi Publishing Corporation, 2014) Baleanu, Dumitru; Trujillo, Juan J.; Ahmad, Bashir
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.
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: 49
Citation - Scopus: 65
Existence and Uniqueness of Solutions to Fractional Differential Equations in the Frame of Generalized Caputo Fractional Derivatives
(Springer, 2018) Gambo, Y. Y.; Ameen, R.; Jarad, Fahd; Abdeljawad, T.
The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607-2619, 2017). Depending on the value of. in the limiting case, the generality of the derivative is that it gives birth to two different fractional derivatives. However, the existence and uniqueness of solutions to fractional differential equations with generalized Caputo fractional derivatives have not been proven. In this paper, Cauchy problems for differential equations with the above derivative in the space of continuously differentiable functions are studied. Nonlinear Volterra type integral equations of the second kind corresponding to the Cauchy problem are presented. Using Banach fixed point theorem, the existence and uniqueness of solution to the considered Cauchy problem is proven based on the results obtained.
Citation - Scopus: 1
Solutions of a Fractional Dirac Equation
(2010) Muslih, S.I.; Agrawal, O.P.; Baleanu, D.
This is a short version of a paper on the solution of a Fractional Dirac Equation (FDE). In this paper, we present two different techniques to obtain a new FDE. The first technique is based on a Fractional Variational Principle (FVP). For completeness and ease in the discussion to follow, we briefly describe the fractional Euler-Lagrange equations, and define a new Lagrangian Density Function to obtain the desired FDE. The second technique we define a new Fractional Klein-Gordon Equation (FKGE) in terms of fractional operators and fractional momenta, and use this equation to obtain the FDE. Our FDE could be of any order. We present eigensolutions for the FDE which are very similar to those for the regular Dirac equation. We give only a brief exposition of the topics here. An extended version of this work will be presented elsewhere. Copyright © 2009 by ASME.

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