Matematik Bölümü Yayın Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413
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Article Citation - WoS: 12Citation - Scopus: 15Novel Precise Solutions and Bifurcation of Traveling Wave Solutions for the Nonlinear Fractional (3+1)-Dimensional Wbbm Equation(World Scientific Publ Co Pte Ltd, 2023) Mehdi, Khush Bukht; Jarad, Fahd; Elbrolosy, Mamdouh E.; Elmandouh, Adel A.; Siddique, ImranThe nonlinear fractional differential equations (FDEs) are composed by mathematical modeling through nonlinear corporeal structures. The study of these kinds of models has an energetic position in different fields of applied sciences. In this study, we observe the dynamical behavior of nonlinear traveling waves for the M-fractional (3+1)-dimensional Wazwaz-Benjamin-Bona-Mohany (WBBM) equation. Novel exact traveling wave solutions in the form of trigonometric, hyperbolic and rational functions are derived using (1/G'), modified (G'/G(2)) and new extended direct algebraic methods with the help of symbolic soft computation. We guarantee that all the obtained results are new and verified the main equation. To promote the essential propagated features, some investigated solutions are exhibited in the form of 2D and 3D graphics by passing on the precise values to the parameters under the constrain conditions, and this provides useful information about the dynamical behavior. Further, bifurcation behavior of nonlinear traveling waves of the proposed equation is studied with the help of bifurcation theory of planar dynamical systems. It is also observed that the proposed equation support the nonlinear solitary wave, periodic wave, kink and antikink waves and most important supernonlinear periodic wave.Article Citation - WoS: 16Citation - Scopus: 15Fractional Hyper-Chaotic System With Complex Dynamics and High Sensitivity: Applications in Engineering(World Scientific Publ Co Pte Ltd, 2024) Yusuf, Abdullahi; Alshomrani, Ali S. S.; Sulaiman, Tukur Abdulkadir; Baleanu, Dumitru; Partohaghighi, MohammadHyper-chaotic systems have useful applications in engineering applications due to their complex dynamics and high sensitivity. This research is supposed to introduce and analyze a new noninteger hyper-chaotic system. To design its fractional model, we consider the Caputo fractional operator. To obtain the approximate solutions of the extracted system under the considered fractional-order derivative, we employ an accurate nonstandard finite difference (NSFD) algorithm. Moreover, the existence and uniqueness of the solutions are provided using the theory of fixed-point. Also, to see the performance of the utilized numerical scheme, we choose different values of fractional orders along with various amounts of the initial conditions (ICs). Graphs of solutions for each case are provided.Article Citation - WoS: 2Citation - Scopus: 2Spectrum of the Q-Schrodinger Equation by Means of the Variational Method Based on the Discrete Q-Hermite I Polynomials(World Scientific Publ Co Pte Ltd, 2021) Turan, Mehmet; Adiguzel, Rezan Sevinik; Calisir, Ayse Dogan; Adlgüzel, Rezan Sevinik; Çallşlr, Ayşe DoǧanIn this work, the q-Schrodinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of q, and the limiting case as q -> 1 is considered. The Rayleigh-Ritz variational method is adopted to the system. The discrete q-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: q-harmonic, purely q-quartic and q-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.Article Citation - WoS: 21Citation - Scopus: 34Applications of Gudermannian Neural Network for Solving the Sitr Fractal System(World Scientific Publ Co Pte Ltd, 2021) Umar, Muhammad; Raja, Muhammad Asif Zahoor; Baleanu, Dumitru; Sabir, ZulqurnainThis study is related to explore the Gudermannian neural network (GNN) for solving a nonlinear SITR COVID-19 fractal system by using the optimization efficiencies of a genetic algorithm (GA), a global search technique and sequential quadratic programming (SQP) and a quick local search scheme, i.e. GNN-GA-SQP. The nonlinear SITR COVID-19 fractal system is dependent on four collections: "susceptible", "infected", "treatment" and "recovered". For the optimization procedures through the GNN-GA-SQP, a merit function is constructed using the nonlinear SITR COVID-19 fractal system and its corresponding initial conditions. The description of each collection of the nonlinear SITR COVID-19 fractal system is provided along with comprehensive detail. The comparison of the achieved numerical result performances of each collection of the nonlinear SITR COVID-19 fractal system is performed with the Adams results to verify the exactness of the designed computational GNN-GA-SQP. The statistical processes based on different operators are presented for 30 independent trials using 5 neurons to authenticate the consistency of the designed computational GNN-GA-SQP. Moreover, the graphs of absolute error (AE), performance indices, and convergence measures along with the boxplots and histograms are also plotted to check the stability, exactness and reliability of the designed computational GNN-GA-SQP.Article Citation - WoS: 18Citation - Scopus: 19A New Generalized Kdv Equation: Its Lump-Type, Complexiton and Soliton Solutions(World Scientific Publ Co Pte Ltd, 2022) Hosseini, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Dehingia, K.A new generalized KdV equation, describing the motions of long waves in shallow water under the gravity field, is considered in this paper. By adopting a series of well-organized methods, the Backlund transformation, the bilinear form and diverse wave structures of the governing model are formally extracted. The exact solutions listed in this paper are categorized as lump-type, complexiton, and soliton solutions. To exhibit the physical mechanism of the obtained solutions, several graphical illustrations are given for particular choices of the involved parameters. As a direct consequence, diverse wave structures given in this paper enrich the studies on the KdV-type equations.Article Citation - WoS: 19Citation - Scopus: 22Approximating System of Ordinary Differential-Algebraic Equations Via Derivative of Legendre Polynomials Operational Matrices(World Scientific Publ Co Pte Ltd, 2023) Abdelhakem, M.; Baleanu, D.; Agarwal, P.; Moussa, HanaaLegendre polynomials' first derivatives have been used as the basis function via the pseudo-Galerkin spectral method. Operational matrices for derivatives have been used and extended to deal with the system of ordinary differential-algebraic equations. An algorithm via those matrices has been designed. The accuracy and efficiency of the proposed algorithm had been shown by two techniques, theoretically, via the boundedness of the approximated expansion and numerically through numerical examples.Article Citation - WoS: 3Citation - Scopus: 9Wave Solutions To the More General (2+1)-Dimensional Boussinesq Equation Arising in Ocean Engineering(World Scientific Publ Co Pte Ltd, 2023) Yusuf, Abdullahi; Alshomrani, Ali S.; Baleanu, Dumitru; Sulaiman, Tukur A.The novel wave profiles for the more general (2+1)-dimensional Boussinesq equation are established in this paper. To get such outstanding results, we employ the potent Sardar sub-equation technique. The recognized explanations for several physical difficulties have been studied. These technological advancements have been proven to be helpful for the transmission of long-wave and high-power communications networks. The circumstances that gave rise to the emergence of these solutions are described in detail. The physical characteristics of the governing equation have been depicted in contour plots and three dimensions.Article Citation - WoS: 4Citation - Scopus: 3Theoretical and Numerical Computations of Convexity Analysis for Fractional Differences Using Lower Boundedness(World Scientific Publ Co Pte Ltd, 2023) Al-Sarairah, Eman; Abdeljawad, Thabet; Chorfi, Nejmeddine; Mohammed, Pshtiwan Othman; Baleanu, DumitruThis study focuses on the analytical and numerical solutions of the convexity analysis for fractional differences with exponential and Mittag-Leffler kernels involving negative and nonnegative lower bounds. In the analytical part of the paper, we will give a new formula for del(2) of the discrete fractional differences, which can be useful to obtain the convexity results. The correlation between the nonnegativity and negativity of both of the discrete fractional differences, ((CFR)(a)del(alpha)f)(t) and ((ABR)(a)del(alpha)f)(t), with the convexity of the functions will be examined. In light of the main lemmas, we will define the two decreasing subsets of (2, 3), namely H-k,H-epsilon and M-k,M-epsilon. The decrease of these sets enables us to obtain the relationship between the negative lower bound of ((CFR)(a)del(alpha)f)(t) and the convexity of the function on a finite time set given by N-a+1(P) := {a + 1, a + 2,..., P}, for some P is an element of Na+1 := {a + 1, a + 2,...}. Besides, the numerical part of the paper is dedicated to examine the validity of the sets H-k,H- is an element of and M-k,M- is an element of in certain regions of the solutions for different values of k and is an element of. For this reason, we will illustrate the domain of the solutions by means of several figures in which the validity of the main theorems are explained.Article Citation - WoS: 13Citation - Scopus: 18On Electro-Osmosis in Peristaltic Blood Flow of Magnetohydrodynamics Carreau Material With Slip and Variable Material Characteristics(World Scientific Publ Co Pte Ltd, 2023) Choudhari, Rajashekhar; Baleanu, Dumitru; Prasad, K., V; Shivaleela; Khan, M. Ijaz; Galal, Ahmed M.; Vaidya, HanumeshThe study of electro-osmosis, peristalsis and heat transfer with numerous slips, such as velocity slip, thermal slip and concentration slip, may be used to construct biomimetic thermal pumping systems at the microscale of interest in physiological transport phenomena. A mathematical model has been developed to investigate magnetohydrodynamics non-Newtonian (Carreau fluid) flow induced by the forces to produce a pressure gradient. The walls of the microchannels erode as they expand. The Poisson and Nernst-Planck equations are used to model electro-osmotic processes. This procedure results in Boltzmann circulation of the electric potential across the electric double layer. The governing equations are simplified by approximations such as a low Reynolds number and a long wavelength. The ND Solver in Mathematica simulates and compares simplified coupled nonlinear governing equations. We investigate novel physical parameters affecting flow, heat transfer and pumping. Additionally, a fundamental peristaltic pumping phenomenon known as trapping is graphically provided and briefly discussed. The model's findings show that the velocity increases as the electric field intensifies, implying that electro-osmosis may improve peristaltic flow.Article Citation - WoS: 7Citation - Scopus: 8Numerical Simulation of the Fractional Diffusion Equation(World Scientific Publ Co Pte Ltd, 2023) Yusuf, Abdullahi; Jarad, Fahd; Sulaiman, Tukur A.; Alquran, Marwan; Partohaghighi, MohammadDuring this paper, a specific type of fractal-fractional diffusion equation is presented by employing the fractal-fractional operator. We present a reliable and accurate operational matrix approach using shifted Chebyshev cardinal functions to solve the considered problem. Also, an operational matrix for the considered derivative is obtained from basic functions. To solve the introduced problem, we convert the main equation into an algebraic system by extracting the operational matrix methods. Graphs of exact and approximate solutions along with error graphs are presented. These figures show how the introduced approach is reliable and accurate. Also, tables are established to illustrate the values of solutions and errors. Finally, a comparison of the solutions at a specific time is given for each test problem.