Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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  • Article
    Citation - Scopus: 7
    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.
  • Editorial
    Advanced Theoretical and Applied Studies of Fractional Differential Equations 2013
    (Hindawi Publishing Corporation, 2014) Baleanu, Dumitru; Trujillo, Juan J.; Ahmad, Bashir
  • Article
    Citation - WoS: 18
    Citation - Scopus: 31
    Solving Fractional Integro-Differential Equations by Aboodh Transform
    (int Scientific Research Publications, 2024) Gunasekar, Tharmalingam; Balasundaram, Hemalatha; Santra, Shyam Sundar; Majumder, Debasish; Baleanu, Dumitru; Raghavendran, Prabakaran
    This study approaches some families of fractional integro-differential equations (FIDEs) using a simple fractional calculus method, which leads to several appealing consequences, including the classical Frobenius method, which is generalized. The method presented here is based mostly on certain general theorems on particular solutions of FIDEs using the Aboodh transform and binomial series extension coefficients. We additionally demonstrate techniques to solve FIDEs.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 4
    Numerical Analysis of Fractional Order Discrete Bloch Equa-Tions
    (int Scientific Research Publications, 2024) Santra, Shyam Sundar; Jayanathan, Leo Amalraj; Baleanu, Dumitru; Murugesan, Meganathan
    By defining a new kind of h-extorial function with constant coefficient, this research seeks to solve discrete fractional Bloch equations. By using an extorial function of the Mittag-Leffler type, we are able to discover the general solutions for the magnetization's Bx, By, and Bz components. These findings demonstrate the innovative method of fractional order Bloch equations. In addition, we offer a graphical representation of our results.(c) 2024 All rights reserved.
  • Article
    Citation - Scopus: 4
    Nonlocal Partial Fractional Evolution Equations With State Dependent Delay
    (Universidad Catolica del Norte, 2023) Baghli-Bendimerad, S.; Benchohra, M.; Karapınar, E.; Lachachi-Merad, N.
    In this work, we propose sufficient conditions guaranteeing an existence result of mild solutions by using the nonlinear Leray-Schauder alternative in Banach spaces combined with the semigroup theory for the class of Caputo partial semilinear fractional evolution equations with finite state-dependent delay and nonlocal conditions. © (2023), (SciELO-Scientific Electronic Library Online). All Rights Reserved.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 6
    Existence and Ulam-Hyers Stability of Mild Solutions for Impulsive Integro-Differential Systems Via Resolvent Operators
    (Amer inst Mathematical Sciences-aims, 2025) Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, Erdal; Bensalem, Abdelhamid
    The aim of this paper is to present existence, Ulam-Hyers-Rassias stability and continuous dependence on initial conditions for the mild solution of impulsive integro-differential systems via resolvent operators. Our analysis is based on fixed point theorem with generalized measures of noncompactness, this approach is combined with the technique that uses convergence to zero matrices in generalized Banach spaces. An example is presented to illustrate the efficiency of the result obtained.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 18
    Analysis of the family of integral equation involving incomplete types of I and Ī-functions
    (Taylor & Francis Ltd, 2023) Bhatter, Sanjay; Jangid, Kamlesh; Kumawat, Shyamsunder; Baleanu, Dumitru; Suthar, D.L.; Purohit, Sunil Dutt
    The present article introduces and studies the Fredholm-type integral equation with an incomplete I-function (IIF) and an incomplete (Formula presented.) -function (I (Formula presented.) F) in its kernel. First, using fractional calculus and the Mellin transform principle, we solve an integral problem involving IIF. The idea of the Mellin transform and fractional calculus is then used to analyse an integral equation using the incomplete (Formula presented.) -function. This is followed by the discovery and investigation of several important exceptional cases. This article's general discoveries may yield new integral equations and solutions. The desired outcomes seem to be very helpful in resolving many real-world problems whose solutions represent different physical phenomena. And also, findings help solve introdifferential, fractional differential, and extended integral equation problems.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 7
    A Fractional Study of Mhd Casson Fluid Motion With Thermal Radiative Flux and Heat Injection/Suction Mechanism Under Ramped Wall Condition: Application of Rabotnov Exponential Kernel
    (Sciendo, 2024) Jarad, Fahd; Riaz, Muhammad Bilal; Rehman, Aziz Ur
    The primary objective of this research is to extend the concept of fractionalized Casson fluid flow. In this study, a comprehensive analysis of magnetohydrodynamic (MHD) natural convective flow of Casson fluid is conducted, focusing on obtaining analytical solutions using the non-integer-order derivative known as the Yang-Abdel-Aty-Cattani (YAC) operator. The YAC operator utilized in this research possesses a more generalized exponential kernel. The fluid flow is examined in the vicinity of an infinitely vertical plate with a characteristic velocity denoted as u(0). The mathematical modelling of the problem incorporates partial differential equations, incorporating Newtonian heating and ramped conditions. To facilitate the analysis, a suitable set of variables is introduced to transform the governing equations into a dimensionless form. The Laplace transform (LT) is then applied to the fractional system of equations, and the obtained results are presented in series form and also expressed in terms of special functions. The study further investigates the influence of relevant parameters, such as alpha, beta, P-r, Q, Gr, M, N-r and K, on the fluid flow to reveal interesting findings. A comparison of different approaches reveals that the YAC method yields superior results compared to existing operators found in the literature. Graphs are generated to illustrate the outcomes effectively. Additionally, the research explores the limiting cases of the Casson and viscous fluid models to derive the classical form from the YAC fractionalized Casson fluid model.
  • Article
    Sequences of Nonlinear Quasi Contractions and Fixed Points
    (Univ Nis, Fac Sci Math, 2022) Chi, Kieu Phuong; Karapinar, Erdal; Thanh, Tran Duc
    In this paper, we state some results on the relationship between the convergence of the nonlinear quasi-contractions and the convergence of their fixed point. The observed results certainly extend some existing results on the topic in the literature, including the results of Nadler and Park. We also furnish an illustrative example to demonstrate the validity of the results expressed.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 12
    Soliton Solutions for Non-Linear Kudryashov's Equation Via Three Integrating Schemes
    (Vinca inst Nuclear Sci, 2021) Mirhosseini-Alizamini, Mehdi; Baleanu, Dumitru; Rezazadeh, Hadi; Inc, Mustafa; Hussain, Majid; Arshed, Saima; Mirhosseini-Alizamini, Seyed Mehdi; Mustafa, I.N.C.
    This paper considers the non-linear Kudryashov's equation, that is an extension of the well-known dual-power law of refractive index and is analog to the generalized version of anti-cubic non-linearity. The model is considered in the presence of full non-linearity. The main objective of this paper is to extract soliton solutions of the proposed model. Three state-of-the-art integration schemes, namely modified auxiliary equation method, the sine-Gordon expansion method and the tanh-coth expansion method have been employed for obtaining the desired soliton solutions.