Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 81Citation - Scopus: 94The Fractional Dynamics of a Linear Triatomic Molecule(Editura Acad Romane, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Defterli, Özlem; Jajarmi, Amin; Defterli, Ozlem; Asad, Jihad H.; MatematikIn this research, we study the dynamical behaviors of a linear triatomic molecule. First, a classical Lagrangian approach is followed which produces the classical equations of motion. Next, the generalized form of the fractional Hamilton equations (FHEs) is formulated in the Caputo sense. A numerical scheme is introduced based on the Euler convolution quadrature rule in order to solve the derived FHEs accurately. For different fractional orders, the numerical simulations are analyzed and investigated. Simulation results indicate that the new aspects of real-world phenomena are better demonstrated by considering flexible models provided within the use of fractional calculus approaches.Article Citation - WoS: 20Citation - Scopus: 22Analytical Treatment of System of Abel Integral Equations by Homotopy Analysis Method(Editura Acad Romane, 2014) Jafarian, A.; Baleanu, Dumitru; Ghaderi, P.; Golmankhaneh, Alireza K.; Baleanu, D.; MatematikAbel equation has important applications in describing the least time for an object which is sliding on surface without friction in uniform gravity, and the classical theory of elasticity of materials is modeled by a system of Abel integral equations. In this manuscript, the homotopy analysis method is presented for obtaining analytical solutions of a system of Abel integral equations as fractional equations. The applied method has lessened the size of calculation and improved the accuracy of solution in the case of the singular Abel integral equation. The illustrated examples and numerical results have proved the assertion.Article Citation - WoS: 19Citation - Scopus: 20Fractional Calculus Analysis of the Cosmic Microwave Background(Editura Acad Romane, 2013) Tenreiro Machado, J. A.; Baleanu, Dumitru; Stefanescu, Petruta; Tintareanu, Ovidiu; Baleanu, Dumitru; MatematikCosmic microwave background (CMB) radiation is the imprint from an early stage of the Universe and investigation of its properties is crucial for understanding the fundamental laws governing the structure and evolution of the Universe. Measurements of the CMB anisotropies are decisive to cosmology, since any cosmological model must explain it. The brightness, strongest at the microwave frequencies, is almost uniform in all directions, but tiny variations reveal a spatial pattern of small anisotropies. Active research is being developed seeking better interpretations of the phenomenon. This paper analyses the recent data in the perspective of fractional calculus. By taking advantage of the inherent memory of fractional operators some hidden properties are captured and described.Article Citation - WoS: 7Citation - Scopus: 8On the New Hadamard Fractional Optimal Control Problems(Sage Publications Ltd, 2023) Tajani, Asmae; Jajarmi, Amin; Baleanu, Dumitru; Zguaid, KhalidThe main goal of this manuscript is to investigate a fractional optimal control problem subject to a dynamical system involving Hadamard fractional derivatives. Necessary conditions for the optimality of the considered problem are derived in terms of the corresponding Euler-Lagrange equations. An iterative method is also proposed to numerically solve the obtained equations from the necessary optimality conditions. Two illustrative examples are considered and simulated in order to show the applicability and efficiency of the proposed method. Numerical simulations show that the used method presents some satisfying results regarding the absolute error values.Article Citation - WoS: 10Citation - Scopus: 11On Nabla Conformable Fractional Hardy-Type Inequalities on Arbitrary Time Scales(Springer, 2021) Baleanu, Dumitru; El-Deeb, Ahmed A.; Makharesh, Samer D.; Nwaeze, Eze R.; Iyiola, Olaniyi S.The main aim of the present article is to introduce some new backward difference -conformable dynamic inequalities of Hardy type on time scales. We present and prove several results using chain rule and Fubini's theorem on time scales. Our results generalize, complement, and extend existing results in the literature. Many special cases of the proposed results, such as new conformable fractional h-sum inequalities, new conformable fractional q-sum inequalities, and new classical conformable fractional integral inequalities, are obtained and analyzed.Article From Eikonal To Antieikonal Approximations: Competition of Scales in the Framework of Schrodinger and Classical Wave Equation(Asme, 2022) Pilar Velasco, M.; Baleanu, Dumitru; Luis Vazquez-Poletti, J.; Jimenez, Salvador; Vazquez, Luis; Vázquez-Poletti, J. Luis; Velasco, M. PilarWe present a description of certain limits associated with the Schrodinger equation, the classical wave equation, and Maxwell equations. Such limits are mainly characterized by the competition of two fundamental scales. More precisely: (1) The competition of an exploratory wavelength and the scale of fluctuations is associated with the media where the propagation takes place. From that, the universal behaviors arise eikonal and anti-eikonal. (2) In the context above, it is specially relevant and promising the study of propagation of electromagnetic waves in a media with a self-similar structure, like a fractal one. These systems offer the suggestive scenario where the eikonal and anti-eikonal behaviors are simultaneous. This kind of study requires large and massive computations that are mainly possible in the framework of the cloud computing. Recently, we started to carry out this task. (3) Finally and as a collateral aspect, we analyze the Planck constant in the interval 0 <= h <= infinity.Article Citation - WoS: 11Citation - Scopus: 13Image Encryption Algorithm Based on New Fractional Beta Chaotic Maps(Tech Science Press, 2022) Natiq, Hayder; Alkhayyat, Ahmed; Farhan, Alaa Kadhim; Al-Saidi, Nadia M. G.; Baleanu, Dumitru; Ibrahim, Rabha W.In this study, a new algorithm of fractional beta chaotic maps is proposed to generate chaotic sequences for image encryption. The proposed technique generates multi random sequences by shuffling the image pixel position. This technique is used to blur the pixels connecting the input and encrypted images and to increase the attack resistance. The proposed algorithm makes the encryption process sophisticated by using fractional chaotic maps, which hold the properties of pseudo-randomness. The fractional beta sequences are utilized to alter the image pixels to decryption attacks. The experimental results proved that the proposed image encryption algorithm successfully encrypted and decrypted the images with the same keys. The output findings indicate that our proposed algorithm has good entropy and low correlation coefficients. This translates to enhanced security against different attacks. A MATLAB programming tool was used to implement and assess the image quality measures. A comparison with other image encryption techniques regarding the visual inspection and signal-to-noise ratio is provided.Article Citation - WoS: 5Citation - Scopus: 6Convoluted Fractional Differentials of Various Forms Utilizing the Generalized Raina's Function Description With Applications(Taylor & Francis Ltd, 2022) Baleanu, Dumitru; Ibrahim, Rabha W.A generalized differential operator utilizing Raina's function is constructed in light of a certain type of fractional calculus. We next use the generalized operators to build a formula for analytic functions of type normalized. Our method is based on the concepts of subordination and superordination. As an application, a class of differential equations involving the suggested operator is studied. As seen, the solution is provided by a certain hypergeometric function. We also create a fractional coefficient differential operator. Its geometric and analytic features are discussed. Finally, we use the Jackson's calculus to expand the Raina's differential operator and investigate its properties in relation to geometric function theory.Article Citation - WoS: 1Citation - Scopus: 4Image Splicing Detection Using Generalized Whittaker Function Descriptor(Tech Science Press, 2023) Al-Shamayleh, Ahmad Sami; Ibrahim, Rabha W.; Baleanu, DumitruImage forgery is a crucial part of the transmission of misinfor-mation, which may be illegal in some jurisdictions. The powerful image editing software has made it nearly impossible to detect altered images with the naked eye. Images must be protected against attempts to manipulate them. Image authentication methods have gained popularity because of their use in multimedia and multimedia networking applications. Attempts were made to address the consequences of image forgeries by creating algorithms for identifying altered images. Because image tampering detection targets processing techniques such as object removal or addition, identifying altered images remains a major challenge in research. In this study, a novel image texture feature extraction model based on the generalized k-symbol Whittaker function (GKSWF) is proposed for better image forgery detection. The proposed method is divided into two stages. The first stage involves feature extraction using the proposed GKSWF model, followed by classification using the "support vector machine" (SVM) to distinguish between authentic and manipulated images. Each extracted feature from an input image is saved in the features database for use in image splicing detection. The proposed GKSWF as a feature extraction model is intended to extract clues of tam-pering texture details based on the probability of image pixel. When tested on publicly available image dataset "CASIA" v2.0 (Chinese Academy of Sciences, Institute of Automation), the proposed model had a 98.60% accuracy rate on the YCbCr (luminance (Y), chroma blue (Cb) and chroma red (Cr)) color spaces in image block size of 8 x 8 pixels. The proposed image authentication model shows great accuracy with a relatively modest dimension feature size, supporting the benefit of utilizing the k-symbol Whittaker function in image authentication algorithms.Article Citation - WoS: 5The Fractional Linear Systems of Equations Within an Operational Approach(Asme, 2013) Saadatmandi, Abbas; Kadem, Abdelouahab; Dehghan, Mehdi; Baleanu, DumitruFractional calculus is a rapidly going area from both experimental and theoretical points of view. As a result new methods and techniques should be developed in order to deal with new types of fractional differential equations. In this paper the operational matrix of fractional derivative together with the tau method are used to solve the linear systems of fractional differential equations. The results of this method are shown by solving three illustrative examples. By comparing the obtained results with the analytic solutions and with the ones provided by three standard methods for solving the fractional differential equations we conclude that our method gave comparable results.