Matematik Bölümü Yayın Koleksiyonu

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Now showing 1 - 10 of 26
  • Article
    Citation - WoS: 12
    Citation - Scopus: 15
    Novel 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, Imran
    The 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: 16
    Citation - Scopus: 15
    Fractional 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, Mohammad
    Hyper-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: 18
    Citation - Scopus: 19
    A 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: 19
    Citation - Scopus: 22
    Approximating 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, Hanaa
    Legendre 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: 3
    Citation - Scopus: 9
    Wave 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: 13
    Citation - Scopus: 18
    On 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, Hanumesh
    The 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: 7
    Citation - Scopus: 8
    Numerical Simulation of the Fractional Diffusion Equation
    (World Scientific Publ Co Pte Ltd, 2023) Yusuf, Abdullahi; Jarad, Fahd; Sulaiman, Tukur A.; Alquran, Marwan; Partohaghighi, Mohammad
    During 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.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 6
    Analysis of Multiple Slip Effects on Mhd Blood Peristaltic Flow of Phan-Thien Nanofluid Through an Asymmetric Channel
    (World Scientific Publ Co Pte Ltd, 2023) Baleanu, Dumitru; Vaidya, Hanumesh; Prasad, K. V.; Khan, M. Ijaz; Bafakeeh, Omar T.; Galal, Ahmed M.; Choudhari, Rajashekhar
    The primary focus of this paper is to model the MHD peristaltic flow of Phan-Thien-Tanner nanofluid in an asymmetric channel while taking into account multiple slip effects. Approximations based on a long wavelength and a low Reynolds number are used to transform the governing partial differential equations into nonlinear and coupled differential equations. It is possible to obtain an exact solution to the problem of the distribution of temperature and the distribution of nanoparticle concentration. The perturbation technique is employed to solve the nonlinear velocity distribution. The graphical analysis illustrates the effects that essential and relevant parameters have on the velocity field, temperature distribution, nanoparticle concentration, skin friction coefficient, Nusselt number, Sherwood number, pressure rise, and trapping phenomena. The results that were obtained are essential to comprehending the rheology of blood.
  • Article
    Citation - WoS: 7
    Citation - Scopus: 9
    Solitons and Complexitons To the (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Model
    (World Scientific Publ Co Pte Ltd, 2019) Li, Yongjin; Inc, Mustafa; Baleanu, Dumitru; Alshomrani, Ali S.; Aliyu, Aliyu Isa
    This paper investigates the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain (HMF) model. The model describes the nonlinear spin dynamics of HMF. By adopting the modified F-Expansion and projective Riccati equation methods, we report the dark, combined dark-bright and envelope optical solitons, complexitons singular solutions of the equation along with the conditions that must be satisfied for solitons to exist. The physical structure of the obtained solutions are shown by graphic illustration in order to give a better understanding on the dynamics of optical solitons.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 6
    Propagation of Diverse Ultrashort Pulses in Optical Fiber To Triki-Biswas Equation and Its Modulation Instability Analysis
    (World Scientific Publ Co Pte Ltd, 2021) Yusuf, Abdullahi; Yusuf, Bashir; Baleanu, Dumitru; Sulaiman, Tukur Abdulkadir
    This paper presents the modulation instability (MI) analysis and the different types of optical soliton solutions of the Triki-Biswas model equation. The aforesaid model equation is the generalization of the derivative nonlinear Schrodinger equation which describes the ultrashort pulse propagation with non-Kerr dispersion. The study is carried out by means of a novel efficient integration scheme. During this work, a sequence of optical solitons is produced that may have an important in optical fiber systems. The results show that the studied model hypothetically has incredibly rich optical soliton solutions. The constraint conditions for valid soliton solutions are also reported. The gained results show that the applied method is efficient, powerful and can be applied to various complex models with the help of representative calculations.