Browsing by Author "Osman, M. S."

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Citation Count: Kumar, Dipankar...et al. (2020). "A Variety of Novel Exact Solutions for Different Models With the Conformable Derivative in Shallow Water", Frontiers in Physics, vol. 8.
A Variety of Novel Exact Solutions for Different Models With the Conformable Derivative in Shallow Water
(2020) Kumar, Dipankar; Kaplan, Melike; Haque, Md. Rabiul; Osman, M. S.; Baleanu, Dumitru; 56389
For different nonlinear time-conformable derivative models, a versatile built-in gadget, namely the generalized exp(-phi(xi))-expansion (GEE) method, is devoted to retrieving different categories of new explicit solutions. These models include the time-fractional approximate long-wave equations, the time-fractional variant-Boussinesq equations, and the time-fractional Wu-Zhang system of equations. The GEE technique is investigated with the help of fractional complex transform and conformable derivative. As a result, we found four types of exact solutions involving hyperbolic function, periodic function, rational functional, and exponential function solutions. The physical significance of the explored solutions depends on the choice of arbitrary parameter values. Finally, we conclude that the GEE method is more effective in establishing the explicit new exact solutions than the exp(-phi(xi))-expansion method.
Citation Count: Lu, D...et al. (2020). "Analytical and Numerical Simulations for the Kinetics of Phase Separation in Iron (Fe–Cr–X (X=Mo,Cu)) Based On Ternary Alloys",Physica A: Statistical Mechanics and Its Applications, Vol. 537.
Analytical and Numerical Simulations for the Kinetics of Phase Separation in Iron (Fe–Cr–X (X=Mo,Cu)) Based On Ternary Alloys
(Elsevier B.V., 2020) Lu, D.; Osman, M. S.; Khater, M. M. A.; Attia, Raghda A. M.; Baleanu, Dumitru; 56389
In this paper, we investigate the physical behavior of the basic elements that related to phase decomposition in ternary alloys of (Fe–Cr–Mo) and (Fe–Cr–Cu) according to analytical and approximate simulation. We study the dynamic of the separation phase for the ternary alloys of iron. The dynamical process of this separation has been described in a mathematical model called the Cahn–Hilliard equation. The minor element behavior in the process has been described by the Cahn–Hilliard equation. It describes the process of phase separation for two components of a binary fluid in ternary alloys of (Fe–Cr–Mo) and (Fe–Cr–Cu). We implement a modified auxiliary equation method and the cubic B-spline scheme on this mathematical model to show the dynamical process of phase separation and the concentration of one of two components in a system. We try obtaining the solitary and approximate solutions of this model to show the relation between the components in this phase. We discuss our solutions in view of a Stefan, Thomas-Windle, and Navier–Stokes models. Whereas, these models describe the motion of viscous fluid substance.
Citation Count: Inan, B...et al. (2020). "Analytical and Numerical Solutions of Mathematical Biology Models: the Newell-Whitehead-Segel and Allen-Cahn Equations",Mathematical Methods In the Applied Sciences, Vol. 43, No. 5, pp. 2588-2600.
Analytical and Numerical Solutions of Mathematical Biology Models: the Newell-Whitehead-Segel and Allen-Cahn Equations
(John Wiley and Sons LTD., 2020) İnan, Bilge; Osman, M. S.; Ak, Turgut; Baleanu, Dumitru; 56389
In this paper, we combine the unified and the explicit exponential finite difference methods to obtain both analytical and numerical solutions for the Newell-Whitehead-Segel–type equations which are very important in mathematical biology. The unified method is utilized to obtain various solitary wave solutions for these equations. Numerical solutions of the specific case studies are investigated by using the explicit exponential finite difference method ensures the accuracy and reliability of the proposed scheme. After obtaining the approximate solutions, convergence analysis and error estimation (the error norms and absolute errors) are presented by comparing these results with the analytical obtained solutions and other methods in the literature through tables and graphs. The obtained analytical and numerical results are in good agreement.
Citation Count: Ali, Khalid K...et al. (2020). "Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model", Chaos Solitons & Fractals, Vol. 139.
Analytical and numerical study of the DNA dynamics arising in oscillator-chain of Peyrard-Bishop model
(2020) Ali, Khalid K.; Cattani, Carlo; Gomez-Aguilar, J. F.; Baleanu, Dumitru; Osman, M. S.; 56389
In this work, we introduce a numerical and analytical study of the Peyrard-Bishop DNA dynamic model equation. This model is studied analytically by hyperbolic and exponential ansatz methods and numerically by finite difference method. A comparison between the results obtained by the analytical methods and the numerical method is investigated. Furthermore, some figures are introduced to show how accurate the solutions will be obtained from the analytical and numerical methods. (C) 2020 Elsevier Ltd. All rights reserved.
Citation Count: Osman, M. S...et al. (2020). "Different Types of Progressive Wave Solutions via the 2D-Chiral Nonlinear Schrodinger Equation", Frontiers in Physics, Vol. 8.
Different Types of Progressive Wave Solutions via the 2D-Chiral Nonlinear Schrodinger Equation
(2020) Osman, M. S.; Baleanu, Dumitru; Tariq, Kalim Ul-Haq; Kaplan, Melike; Younis, Muhammad; Rizvi, Syed Tahir Raza; 56389
A versatile integration tool, namely the protracted (or extended) Fan sub-equation (PFS-E) technique, is devoted to retrieving a variety of solutions for different models in many fields of the sciences. This essay presents the dynamics of progressive wave solutions via the 2D-chiral nonlinear Schrodinger (2D-CNLS) equation. The solutions acquired comprise dark optical solitons, periodic solitons, singular dark (bright) solitons, and singular periodic solutions. By comparing the results gained in this work with other literature, it can be noticed that the PFS-E method is an useful technique for finding solutions to other similar problems. Furthermore, some new types of solutions are revealed that will help us better understand the dynamic behaviors of the 2D-CNLS model.
Citation Count: Osman, M. S...et al. (2020). "Double-wave solutions and Lie symmetry analysis to the (2+1)-dimensional coupled Burgers equations", Chinese Journal of Physics, Vol. 63, pp. 122-129.
Double-wave solutions and Lie symmetry analysis to the (2+1)-dimensional coupled Burgers equations
(2020) Osman, M. S.; Baleanu, Dumitru; Adem, A. R.; Hosseini, K.; Mirzazadeh, M.; Eslami, M.; 56389
This paper investigates the (2 + 1)-dimensional coupled Burgers equations (CBEs) which is an important nonlinear physical model. In this respect, by making use of the generalized unified method (GUM), a series of double-wave solutions of the (2 + 1)-dimensional coupled Burgers equations are derived. The Lie symmetry technique (LST) is also utilized for the symmetry reductions of the (2 + 1)-dimensional coupled Burgers equations and extracting a non-traveling wave solution. Through some figures, we discussed the wave structures of the double-wave solutions of the CBEs for different values of parameters in these solutions.
Citation Count: Chanbari, Behzad; Osman, M. S.; Baleanu, Dumitru, "Generalized exponential rational function method for extended Zakharov-Kuzetsov equation with conformable derivative", Modern Physics Letters A, Vol. 34, no. 20, (2019).
Generalized exponential rational function method for extended Zakharov-Kuzetsov equation with conformable derivative
(World Scientific Publ CO PTE LTD, 2019) Chanbari, Behzad; Osman, M. S.; Baleanu, Dumitru; 56389
In this paper, new analytical obliquely propagating wave solutions for the time fractional extended Zakharov-Kuzetsov (FEZK) equation of conformable derivative are investigated. By using the main properties of the conformable derivative, the FEZK equation is transformed into integer-order differential equations, and the reduced equations are solved via the generalized exponential rational function method (GERFM). The shape and features for the resulting solutions are illustrated through three-dimensional (3D) plots and corresponding contour plots for various values of the free parameters.
Citation Count: Lu, D...et al. (2019). "New analytical wave structures for the (3", Results in Physics, Vol. 14.
New analytical wave structures for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq models and their applications
(Elsevier, 2019) Lu, D.; Tariq, K.U.; Osman, M. S.; Baleanu, Dumitru; Younisg, M.; Khatera, M.M.A.; 56389
Different types of soliton wave solutions for the (3 + 1)-dimensional Kadomtsev-Petviashvili and the generalized Boussinesq equations are investigated via the solitary wave ansatz method. These solutions are classified into three categories, namely solitary wave, shock wave, and singular wave solutions. The corresponding integrability criteria, termed as constraint conditions, obviously arise from the study. Moreover, the influences of the free parameters and interaction properties in these solutions are discussed graphically for physical interests and possible applications.
Citation Count: Park, Choonkil...et al. (2020). "Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg-de Vries equations". ADVANCES IN DIFFERENCE EQUATIONS. Vol: 2020, No: 1.
Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg-de Vries equations
(2020) Park, Choonkil; Nuruddeen, R., I; Ali, Khalid K.; Muhammad, Lawal; Osman, M. S.; Baleanu, Dumitru; 56389
This paper aims to investigate the class of fifth-order Korteweg-de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.
Citation Count: Baleanu, Dumitru; Machado, J. A. T.; Osman, M. S., "On Nonautonomous Complex Wave Solutions Described By The Coupled Schrodinger-Boussinesq Equation With Variable-Coefficients", Optical and Quantum Electronics, 50, No. 2, (2018).
On Nonautonomous Complex Wave Solutions Described By The Coupled Schrodinger-Boussinesq Equation With Variable-Coefficients
(Springer, 2018) Osman, M. S.; Machado, J. A. Tenreiro; Baleanu, Dumitru; 56389
This paper investigates the coupled Schrodinger-Boussinesq equation with variable-coefficients using the unified method. New nonautonomous complex wave solutions are obtained and classified into two categories, namely polynomial function and rational function solutions. For the polynomial functions emerge the complex solitary, complex soliton and complex elliptic wave solutions, while for the rational function are observed complex periodic rational and complex hyperbolic rational wave solutions. The physical insight and the dynamical behavior of the solutions describing the wave propagation in laser or plasma physics are discussed and analysed for different choices of the arbitrary functions in the solutions.
Citation Count: Srivastava, H. M...et al. (2020). "Traveling wave solutions to nonlinear directional couplers by modified Kudryashov method", Physica Scripta, Vol. 95, No. 7.
Traveling wave solutions to nonlinear directional couplers by modified Kudryashov method
(2020) Srivastava, H. M.; Baleanu, Dumitru; Machado, J. A. T.; Osman, M. S.; Rezazadeh, H.; Arshed, S.; Gunerhan, H.; 56389
This work finds several new traveling wave solutions for nonlinear directional couplers with optical metamaterials by means of the modified Kudryashov method. This model can be used to distribute light from a main fiber into one or more branch fibers. Two forms of optical couplers are considered, namely the twin- and multiple- core couplers. These couplers, which have applications as intensity-dependent switches and as limiters, are studied with four nonlinear items namely the Kerr, power, parabolic, and dual-power laws. The restrictions on the parameters for the existence of solutions are also examined. The 3D- and 2D figures are introduced to discuss the physical meaning for some of the gained solutions. The performance of the method shows the adequacy , power, and ability for applying to many other nonlinear evolution models.