Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Some more bounded and singular pulses of a generalized scale-invariant analogue of the Korteweg–de Vries equation(2023) Saifullah, Sayed; Alqarni, M.M.; Ahmad, Shabir; Baleanu, Dumitru; Khan, Meraj Ali; Mahmoud, Emad E.We investigate a generalized scale-invariant analogue of the Korteweg–de Vries (KdV) equation, establishing a connection with the recently discovered short-wave intermediate dispersive variable (SIdV) equation. To conduct a comprehensive analysis, we employ the Generalized Kudryashov Technique (KT), Modified KT, and the sine–cosine method. Through the application of these advanced methods, a diverse range of traveling wave solutions is derived, encompassing both bounded and singular types. Among these solutions are dark and bell-shaped waves, as well as periodic waves. Significantly, our investigation reveals novel solutions that have not been previously documented in existing literature. These findings present novel contributions to the field and offer potential applications in various physical phenomena, enhancing our understanding of nonlinear wave equations.Article Solitary wave solutions to Gardner equation using improved tan(Ω(Υ)/2-expansion method(2023) Akram, Ghazala; Sadaf, Maasoomah; Dawood, Mirfa; Abbas, Muhammad; Baleanu, DumitruIn this study, the improved tan(Ω(Υ)/2-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.Article Citation - WoS: 3Citation - Scopus: 3Simulating systems of Ito? SDEs with split-step (?, ?)-Milstein scheme(Amer Inst Mathematical Sciences-AIMS, 2022) Ranjbar, Hassan; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, KazemIn the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (alpha, beta)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters alpha, beta. Finally, numerical examples illustrate the effectiveness of the theoretical results.Article Citation - WoS: 13Citation - Scopus: 17Nonautonomous lump-periodic and analytical solutions tothe (3+1)-dimensional generalized Kadomtsev-Petviashviliequation(Springer, 2023) Alquran, Marwan; Sulaiman, Tukur Abdulkadir; Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, DumitruThis work establishes the lump periodic and exact traveling wave solutions for the (3 + 1)-dimensional generalized Kadomtsev-Petviashvili equation. We use the Hirota bilinear method, as well as the robust integration techniques tanh-coth expansion and rational sine-cosine, to provide such innovative solutions. In order to explain specific physical difficulties, innovative lump periodic and analytical solutions have been investigated. These discoveries have been proven to be useful in the transmission of long-wave and high-power communications networks. It is important to highlight that the results given in thiswork depict new features and reflect previously unknown physical dynamics for the governing model.Article An e ffective method for solving nonlinear integral equations involving the Riemann-Liouville fractional operator(2023) Paul, Supriya Kumar; Mishra, Lakshmi Narayan; Mishra, Vishnu Narayan; Baleanu, DumitruIn this paper, under some conditions in the Banach space C([0; beta];R), we establish the existence and uniqueness of the solution for the nonlinear integral equations involving the Riemann-Liouville fractional operator (RLFO). To establish the requirements for the existence and uniqueness of solutions, we apply the Leray-Schauder alternative and Banach's fixed point theorem. We analyze Hyers-Ulam-Rassias (H-U-R) and Hyers-Ulam (H-U) stability for the considered integral equations involving the RLFO in the space C([0; beta];R). Also, we propose an e ffective and e fficient computational method based on Laguerre polynomials to get the approximate numerical solutions of integral equations involving the RLFO. Five examples are given to interpret the method.Article Simulating systems of Itô SDEs with split-step (α, β)-Milstein scheme(2023) Ranjbar, Hassan; Torkzadeh, Leila; Baleanu, Dumitru; Nouri, KazemIn the present study, we provide a new approximation scheme for solving stochastic differential equations based on the explicit Milstein scheme. Under sufficient conditions, we prove that the split-step (α, β)-Milstein scheme strongly convergence to the exact solution with order 1.0 in mean-square sense. The mean-square stability of our scheme for a linear stochastic differential equation with single and multiplicative commutative noise terms is studied. Stability analysis shows that the mean-square stability of our proposed scheme contains the mean-square stability region of the linear scalar test equation for suitable values of parameters α, β. Finally, numerical examples illustrate the effectiveness of the theoretical results.Article Fixed point results in C*-algebra-valued bipolar metric spaces with an application(2023) Mani, Gunaseelan; Gnanaprakasam, Arul Joseph; Işık, Hüseyin; Jarad, FahdIn this work, we prove existence and uniqueness fixed point theorems under Banach and Kannan type contractions on C*-algebra-valued bipolar metric spaces. To strengthen our main results, an appropriate example and an effective application are presented.Article Discussions on Proinov- Cb -Contraction Mapping on b -Metric Space(2023) Karapınar, Erdal; Fulga, AndreeaIn the present paper, we introduce the notion of Proinov-Cb-contraction mapping and we discuss it within the most interesting abstract structure, namely, b-metric spaces. We further take into consideration the necessary conditions to guarantee the existence and uniqueness of fixed points for such mappings, as well as indicate the validity of the main results by providing illustrative examples.Article Accurate novel explicit complex wave solutions of the (2+1)-dimensional Chiral nonlinear Schrodinger equation(2021) Alshahrani, B.; Yakout, H. A.; Khater, Mostafa M. A.; Abdel-Aty, Abdel-Haleem; Mahmoud, Emad E.; Baleanu, Dumitru; Eleuch, HichemThis manuscript investigates the accuracy of the solitary wave solutions of the (2+1)-dimensional nonlinear Chiral Schrodinger ((2+1)-D CNLS) equation that are constructed by employing two recent analytical techniques (modified Khater (MKhat) and modified Jacobian expansion (MJE) methods). This investigation is based on evaluating the initial and boundary conditions through the obtained analytical solutions then employing the Adomian decomposition (AD) method to evaluate the approximate solutions of the (2+1)-D CNLS equation. This framework gives the ability to get large complex traveling wave solutions of the considered model and shows the superiority of the employed computational schemes by comparing the absolute error for each of them. The handled model describes the edge states of the fractional quantum hall effect. Many novel solutions are obtained with various formulas such as trigonometric, rational, and hyperbolic to the studied model. For more illustration of the results, some solutions are displayed in 2D, 3D, and density plots.Article Multidetermination of thiamine HCl and pyridoxine HCl in their mixture using continuous daubechies and biorthogonal wavelet analysis(Elsevier, 2003) Dinç, E.; Baleanu, DumitruA new graphical method based on the one-dimensional wavelet transform (WT) was proposed and tested on mixture of thiamine hydrochloride (THI) and pyridoxine hydrochloride (PYR) in the presence of strongly overlapping signals. We selected from the data of the UV-VIS absorption spectra a signal consisting of 1150 points corresponding to the concentration range 8-32 mg ml(-1) for each vitamin and we subjected it to Daubechies8 (DAUB8) and Biorthogonal6.8 (BIOR6.8) wavelet transforms. Since the peaks of the transformed signals were bigger than original ones a zero crossing method was applied to obtain the calibration graphs. In addition, the validity of Beer-Lambert law was assumed for the transformed signals. An appropriate scale setting was choosing to obtain an alternative calibration for each method. MATLAB 6.5 software was used for one-dimensional wavelet analysis and the basic concepts about wavelet method were given. The obtained results were successfully compared among each other as well as with those obtained by other literature methods. The method developed in this paper is rapid, easy to apply, not expensive and it is suitable for analyzing of the overlapping signals of compounds in their mixtures without any chemical pre-treatment. (C) 2002 Elsevier Science B.V. All rights reserved.
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