Browsing by Author "Osman, M. S."

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Citation - WoS: 24
Citation - Scopus: 30
Advanced Exact Solutions To the Nano-Ionic Currents Equation Through Mts and the Soliton Equation Containing the Rlc Transmission Line
(Springer Heidelberg, 2023) Miah, M. Mamun; Iqbal, M. Ashik; Alshehri, Hashim M.; Baleanu, Dumitru; Osman, M. S.; Chowdhury, M. Akher; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this study, the double (G '/G, 1/G)-expansion method is utilized for illustrating the improved explicit integral solutions for the two of nonlinear evolution equations. To expose the importance and convenience of our assumed method, we herein presume two models, namely the nano-ionic currents equation and the soliton equation. The exact solutions are generated with the aid of our proposed method in such a manner that the solutions involve to the rational, trigonometric, and hyperbolic functions for the first presumed nonlinear equation as well as the trigonometric and hyperbolic functions for the second one with meaningful symbols that promote some unique periodic and solitary solutions. The method used here is an extension of the (G '/G)-expansion method to rediscover all known solutions. We offer 2D and 3D charts of the various recovery solutions to better highlight our findings. Finally, we compared our results with those of earlier solutions.
Citation - WoS: 3
Citation - Scopus: 5
Analytical and Numerical Simulations for the Kinetics of Phase Separation in Iron (fe-Cr (X = Mo, Cu)) Based on Ternary Alloys (Vol 537c, 122634, 2019)
(Elsevier, 2021) Lu, D.; Osman, M. S.; Khater, M. M. A.; Attia, R. A. M.; Baleanu, D.; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Citation - WoS: 78
Citation - Scopus: 77
Analytical and Numerical Simulations for the Kinetics of Phase Separation in Iron (fe-Cr (X=mo, Cu)) Based on Ternary Alloys
(Elsevier, 2020) Osman, M. S.; Khater, M. M. A.; Attia, R. A. M.; Baleanu, D.; Lu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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. (C) 2019 Elsevier B.V. All rights reserved.
Citation - WoS: 100
Citation - Scopus: 119
Analytical and Numerical Study of the Dna Dynamics Arising in Oscillator-Chain of Peyrard-Bishop Model
(Pergamon-elsevier Science Ltd, 2020) Cattani, Carlo; Gomez-Aguilar, J. F.; Baleanu, Dumitru; Osman, M. S.; Ali, Khalid K.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 37
Citation - Scopus: 42
Different Types of Progressive Wave Solutions Via the 2d-Chiral Nonlinear Schrodinger Equation
(Frontiers Media Sa, 2020) Baleanu, Dumitru; Tariq, Kalim Ul-Haq; Kaplan, Melike; Younis, Muhammad; Rizvi, Syed Tahir Raza; Osman, M. S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 117
Citation - Scopus: 127
Double-Wave Solutions and Lie Symmetry Analysis To the (2+1)-Dimensional Coupled Burgers Equations
(Elsevier, 2020) Eslami, M.; Osman, M. S.; Baleanu, D.; Adem, A. R.; Hosseini, K.; Mirzazadeh, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 142
Citation - Scopus: 164
Generalized Exponential Rational Function Method for Extended Zakharov-Kuzetsov Equation With Conformable Derivative
(World Scientific Publ Co Pte Ltd, 2019) Osman, M. S.; Baleanu, Dumitru; Chanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 26
Citation - Scopus: 30
Inelastic Soliton Wave Solutions With Different Geometrical Structures To Fractional Order Nonlinear Evolution Equations
(Elsevier, 2022) Baleanu, Dumitru; Sadiya, Umme; Arefin, Mohammad Asif; Uddin, M. Hafiz; Elamin, Mahjoub A.; Osman, M. S.; Adel, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The general time fractional Burger- Fisher (TF-BF) and the space-time regularized long-wave (STF-RLW) equations are considered as examples of gravitational water waves in cold plasma as well as so many areas. The above equations are used in nonlinear science and engineering to study long waves in seas and harbors that travel in just one direction. First, the two equations are transformed to ODEs by applying a fractional complex transform along with characteristics of confirmable fractional derivative (CFD). Then, the extended tanh-function (ETF) approach is investigated to find a variety of analytical solutions with different geometrical wave structures the mentioned models. The results are in the form of kink, one-, two-, multiple-solitons solutions, and other types sketched in 2D, 3D, and contour patterns.
Citation - WoS: 84
Citation - Scopus: 88
New Analytical Wave Structures for the (3
(Elsevier, 2019) Tariq, K. U.; Osman, M. S.; Baleanu, D.; Younis, M.; Khater, M. M. A.; Lu, D.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 39
Citation - Scopus: 44
New Soliton Solutions of the Mzk Equation and the Gerdjikov-Ivanov Equation by Employing the Double (g?/G,1 Method
(Elsevier, 2023) Baleanu, Dumitru; Miah, M. Mamun; Ali, H. M. Shahadat; Alshehri, Hashim M.; Osman, M. S.; Iqbal, M. Ashik; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In the electrical transmission lines, the processing of cable signals distribution, computer networks, high-speed computer databases and discrete networks can be investigated by the modified Zakharov-Kuznetsov (mZK) equation as a data link propagation control model in the study of nonlinear Schro center dot dinger type equations as well as in the analysis of the generalized stationary Gardner equation. The proposed Gerdjikov-Ivanov model can be used in the field of nonlinear optics, weakly nonlinear dispersion water waves, quantum field theory etc. In this work, we developed complete traveling wave solutions with specific t-type, kink type, bell-type, singular solu-tions, and periodic singular solutions to the proposed mZK equation and the Gerdjikov-Ivanov equation with the aid of the double (G '/G,1/G)-expansion method. These settled solutions are very reliable, durable, and authentic which can measure the fluid velocity and fluid density in the electrically conductive fluid and be able to analysis of the flow of current and voltage of long-distance electrical transmission lines too. These traveling wave so-lutions are available in a closed format and make them easy to use. The proposed method is consistent with the abstraction of traveling wave solutions.
Citation - WoS: 34
Citation - Scopus: 40
A Novel Analytical Algorithm for Generalized Fifth-Order Time-Fractional Nonlinear Evolution Equations With Conformable Time Derivative Arising in Shallow Water Waves
(Elsevier, 2022) Al-Smadi, Mohammed; Almusawa, Hassan; Baleanu, Dumitru; Hayat, Tasawar; Alhodaly, Mohammed; Osman, M. S.; Abu Arqub, Omar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The purpose of this research is to study, investigate, and analyze a class of temporal time-FNEE models with time-FCDs that are indispensable in numerous nonlinear wave propagation phenomena. For this purpose, an efficient semi-analytical algorithm is developed and designed in view of the residual error terms for solving a class of fifth-order time-FCKdVEs. The analytical solutions of a dynamic wavefunction of the fractional Ito, Sawada-Kotera, Lax's Korteweg-de Vries, Caudrey-Dodd-Gibbon, and Kaup-Kupershmidt equations are provided in the form of a convergent conformable time-fractional series. The related consequences are discussed both theoretically as well as numerically considering the conformable sense. In this direction, convergence analysis and error estimates of the developed algorithm are studied and analyzed as well. Concerning the considered models, specific unidirectional physical experiments are given in a finite compact regime to confirm the theoretical aspects and to demonstrate the superiority of the novel algorithm compared to the other existing numerical methods. Moreover, some representative results are presented in two- and three-dimensional graphs, whilst dynamic behaviors of fractional parameters are reported for several alpha values. From the practical viewpoint, the archived simulations and consequences justify that the iterative algorithm is a straightforward and appropriate tool with computational efficiency for long-wavelength solutions of nonlinear time-FPDEs in physical phenomena. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University
Citation - WoS: 91
Citation - Scopus: 98
Novel Hyperbolic and Exponential Ansatz Methods To the Fractional Fifth-Order Korteweg-De Vries Equations
(Springer, 2020) Nuruddeen, R., I; Ali, Khalid K.; Muhammad, Lawal; Osman, M. S.; Baleanu, Dumitru; Park, Choonkil; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 30
Citation - Scopus: 48
A Numerical Combined Algorithm in Cubic B-Spline Method and Finite Difference Technique for the Time-Fractional Nonlinear Diffusion Wave Equation With Reaction and Damping Terms
(Elsevier, 2022) Abu Arqub, Omar; Tayebi, Soumia; Baleanu, Dumitru; Osman, M. S.; Mahmoud, W.; Alsulami, Hamed; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The applications of the diffusion wave model of a time-fractional kind with damping and reaction terms can occur within classical physics. This quantification of the activity can measure the diagnosis of mechanical waves and light waves. The goal of this work is to predict and construct numerical solutions for such a diffusion model based on the uniform cubic B-spline functions. The Caputo time-fractional derivative has been estimated using the standard finite difference technique, whilst, the uniform cubic B-spline functions have been employed to achieve spatial discretization. The convergence of the suggested blueprint is discussed in detail. To assert the efficiency and authenticity of the study, we compute the approximate solutions for a couple of applications of the diffusion model in electromagnetics and fluid dynamics. To show the mathematical simulation, several tables and graphs are shown, and it was found that the graphical representations and their physical explanations describe the behavior of the solutions lucidly. The key benefit of the resultant scheme is that the algorithm is straightforward and makes it simple to implement as utilized in the highlight and conclusion part.
Citation - WoS: 48
Citation - Scopus: 65
On Beta-Time Fractional Biological Population Model With Abundant Solitary Wave Structures
(Elsevier, 2022) Nisar, Kottakkaran Sooppy; Ciancio, Armando; Ali, Khalid K.; Osman, M. S.; Cattani, Carlo; Baleanu, Dumitru; Azeem, M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The ongoing study deals with various forms of solutions for the biological population model with a novel beta-time derivative operators. This model is very conducive to explain the enlargement of viruses, parasites and diseases. This configuration of the aforesaid classical scheme is scouted for its new solutions especially in soliton shape via two of the well known analytical strategies, namely: the extended Sinh-Gordon equation expansion method (EShGEEM) and the Expa function method. These soliton solutions suggest that these methods have widened the scope for generating solitary waves and other solutions of fractional differential equations. Different types of soliton solutions will be gained such as dark, bright and singular solitons solutions with certain conditions. Furthermore, the obtained results can also be used in describing the biological population model in some better way. The numerical solution for the model is obtained using the finite difference method. The numerical simulations of some selected results are also given through their physical explanations. To the best of our knowledge, No previous literature discussed this model through the application of the EShGEEM and the Expa function method and supported their new obtained results by numerical analysis. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).
Citation - WoS: 20
Citation - Scopus: 20
On Distinctive Solitons Type Solutions for Some Important Nonlinear Schrodinger Equations
(Springer, 2021) Machado, J. A. T.; Baleanu, D.; Zafar, A.; Raheel, M.; Osman, M. S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The extended Jacobi elliptic function expansion (EJEFE) method is used to retrieve several types of optical solitons of two nonlinear Schrodinger equations, namely the Heisenberg ferromagnetic spin chains and Alfven envelop equations. The obtained traveling wave solutions and the corresponding plots are analysed by means of the symbolic package Mathematica. The solutions show that the proposed strategy is effective and reliable for solving different types of nonlinear differential equations.
Citation - WoS: 85
Citation - Scopus: 82
On Nonautonomous Complex Wave Solutions Described by the Coupled Schrodinger-Boussinesq Equation With Variable-Coefficients
(Springer, 2018) Machado, J. A. T.; Baleanu, Dumitru; Osman, M. S.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - WoS: 31
Citation - Scopus: 37
Physically Significant Wave Solutions To the Riemann Wave Equations and the Landau-Ginsburg Equation
(Elsevier, 2021) Aktar, Most Shewly; Uddin, M. Hafiz; Akbar, M. Ali; Baleanu, Dumitru; Osman, M. S.; Barman, Hemonta Kumar; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The nonlinear Riemann wave equations (RWEs) and the Landau-Ginsburg-Higgs (LGH) equation are related to plasma electrostatic waves, ion-cyclotron wave electrostatic potential, superconductivity, and drift coherent ioncyclotron waves in centrifugally inhomogeneous plasma. In this article, the interactions between the maximum order linear and nonlinear factors are balanced to compute realistic soliton solutions to the formerly stated equations in terms of hyperbolic functions. The linear and nonlinear effects rheostat the structure of the wave profiles, which vary in response to changes in the subjective parameters combined with the solutions. The established solutions to the aforementioned models using the extended tanh scheme are descriptive, typical, and consistent, and include standard soliton shapes such as bright soliton, dark soliton, compacton, peakon, periodic, and others that can be used to analyze in ion-acoustic and magneto-sound waves in plasma, homogeneous, and stationary media, particularly in the propagation of tidal and tsunami waves.
Citation - WoS: 38
Citation - Scopus: 45
Protracted Study on a Real Physical Phenomenon Generated by Media Inhomogeneities
(Elsevier, 2021) Ali, Khalid K.; Wazwaz, Abdul-Majid; Mehanna, M. S.; Baleanu, D.; Osman, M. S.; Almusawa, Hassan; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, we study the dynamical behavior for a real physical application due to the inhomogeneities of media via analytical and numerical approaches. This phenomenon is described by the 3D Date-Jimbo-Kashiwara-Miwa (3D-DJKM) equation. For analytical techniques, three different methods are performed to get hyperbolic, trigonometric and rational functions solutions. After that, the obtained solutions are graphically depicted through 2D-and 3D-plots and numerically compared via the finite difference algorithm to check the precision of the proposed methods.
Citation - WoS: 27
Citation - Scopus: 27
Solitons and Jacobi Elliptic Function Solutions To the Complex Ginzburg-Landau Equation
(Frontiers Media Sa, 2020) Hosseini, Kamyar; Mirzazadeh, Mohammad; Osman, M. S.; Al Qurashi, Maysaa; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The complex Ginzburg-Landau (CGL) equation which describes the soliton propagation in the presence of the detuning factor is firstly considered; then its solitons as well as Jacobi elliptic function solutions are obtained systematically using a modified Jacobi elliptic expansion method. In special cases, several dark and bright soliton solutions to the CGL equation are retrieved when the modulus of ellipticity approaches unity. The results presented in the current work can help to complete previous studies on the complex Ginzburg-Landau equation.
Citation - WoS: 147
Traveling Wave Solutions To Nonlinear Directional Couplers by Modified Kudryashov Method
(Iop Publishing Ltd, 2020) Baleanu, D.; Machado, J. A. T.; Osman, M. S.; Rezazadeh, H.; Arshed, S.; Gunerhan, H.; Srivastava, H. M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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.