Matematik Bölümü Yayın Koleksiyonu
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Article Citation - Scopus: 7COVID-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.Article Citation - WoS: 30Citation - Scopus: 31Heat and Mass Transport Impact on MHD Second-Grade Fluid: A Comparative Analysis of Fractional Operators(Wiley, 2021) Rehman, Aziz Ur; Riaz, Muhammad Bilal; Akgul, Ali; Saeed, Syed Tauseef; Baleanu, DumitruThe effect of the magnetic flux plays a major role in convective flow. The process of heat transfer is accompanied by a mass transfer process; for instance, condensation, evaporation, and chemical process. Due to the applications of the heat and mass transfer combined effects in different fields, the main aim of this paper is to do a comprehensive analysis of heat and mass transfer of magnetohydrodynamic (MHD) unsteady second-grade fluid in the presence of ramped conditions. The new governing equations of MHD second-grade fluid have been fractionalized by means of singular and nonsingular differentiable operators. To have an accurate physical significance of imposed conditions on the geometry of second-grade fluid, the constant concentration with ramped temperature and ramped velocity is considered. The fractional solutions of temperature, concentration, and velocity have been investigated by means of integral transform and inversion algorithm. The influence of physical parameters and flow is analyzed graphically via computational software (MATHCAD-15). The velocity profile decreases by increasing the Prandtl number. The existence of a Prandtl number may reflect the control of the thickness and enlargement of the thermal effect.Article Citation - WoS: 6Citation - Scopus: 6Modeling the Transmission Dynamics of Middle Eastern Respiratory Syndrome Coronavirus with the Impact of Media Coverage(Elsevier, 2021) Fatima, BiBi; Alqudah, Manar A.; Zaman, Gul; Jarad, Fahd; Abdeljawad, ThabetMiddle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R-0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.Article Citation - WoS: 1Citation - Scopus: 2Testing the Equality of Several Independent Stationary and Non-Stationary Time Series Models with Fractional Brownian Motion Errors(Elsevier, 2021) Mahmoudi, Mohammad Reza; Baleanu, Dumitru; Qasem, Sultan Noman; Mosavi, Amirhosein; Band, Shahab S.; S. Band, ShahabThis work is devoted to apply the parametric and nonparametric techniques to construct test of hypothesis about the equality of the probabilistic behaviors of several time series models with fractional Brownian motion errors fitted on several independent datasets. The accuracy and power of the introduced method are studied using the simulated and real datasets. The results indicate that the introduced approach is more powerful than other alternative approaches, in non-stationary cases. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Article Citation - WoS: 180Citation - Scopus: 192On Fractional Calculus with General Analytic Kernels(Elsevier Science Inc, 2019) Fernandez, Arran; Ozarslan, Mehmet Ali; Baleanu, DumitruMany possible definitions have been proposed for fractional derivatives and integrals, starting from the classical Riemann-Liouville formula and its generalisations and modifying it by replacing the power function kernel with other kernel functions. We demonstrate, under some assumptions, how all of these modifications can be considered as special cases of a single, unifying, model of fractional calculus. We provide a fundamental connection with classical fractional calculus by writing these general fractional operators in terms of the original Riemann-Liouville fractional integral operator. We also consider inversion properties of the new operators, prove analogues of the Leibniz and chain rules in this model of fractional calculus, and solve some fractional differential equations using the new operators. (C) 2019 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3Existence Results for Block Matrix Operator of Fractional Orders in Banach Algebras(MDPI, 2019) Hashem, Hind; El-Sayed, Ahmed; Baleanu, DumitruThis paper is concerned with proving the existence of solutions for a coupled system of quadratic integral equations of fractional order in Banach algebras. This result is a direct application of a fixed point theorem of Banach algebras. Some particular cases, examples and remarks are illustrated. Finally, the stability of solutions for that coupled system are studied.Article Citation - WoS: 51Citation - Scopus: 66Existence 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.Article Citation - WoS: 3Citation - Scopus: 2Surface Terms, Angular Momentum and Hamilton-Jacobi Formalism(Soc Italiana Fisica, 2003) Güler, Y; Baleanu, Dumitru; Baleanu, D; Cenk, M; MatematikQuadratic Lagrangians are introduced adding surface terms to a free-particle Lagrangian. Geodesic equations are used in the context of the Hamilton-Jacobi formulation of a constrained system. The manifold structure induced by the quadratic Lagrangian is investigated.Article Citation - WoS: 36Citation - Scopus: 41Numerical Treatment of Coupled Nonlinear Hyperbolic Klein-Gordon Equations(Editura Acad Romane, 2014) Doha, E. H.; Baleanu, Dumitru; Bhrawy, A. H.; Baleanu, D.; Abdelkawy, M. A.; MatematikA semi-analytical solution based on a Jacobi-Gauss-Lobatto collocation (J-GL-C) method is proposed and developed for the numerical solution of the spatial variable for two nonlinear coupled Klein-Gordon (KG) partial differential equations. The general Jacobi-Gauss-Lobatto points are used as collocation nodes in this approach. The main characteristic behind the J-GL-C approach is that it reduces such problems to solve a system of ordinary differential equations (SODEs) in time. This system is solved by diagonally-implicit Runge-Kutta-Nystrom scheme. Numerical results show that the proposed algorithm is efficient, accurate, and compare favorably with the analytical solutions.Article Citation - Scopus: 4On Mild Solution of Abstract Neutral Fractional Order Impulsive Differential Equations With Infinite Delay(Eudoxus Press, LLC, 2018) Anguraj, A.; Baleanu, Dumitru; Kanjanadevi, S.; Baleanu, D.; MatematikWe prove the existence and uniqueness of fractional neutral impulsive differential equations with infinite delay via contraction mapping principle and fixed point technique for condensing map. We use the resolvent operator technique for integral equations to make the mild solution of the problem more appropriate. © 2018 by Eudoxus Press, LLC. All rights reserved.