Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 35Citation - Scopus: 53A 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, HamedThe 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.Article Citation - WoS: 26Citation - Scopus: 30Inelastic 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.; Hafiz Uddin, M.; Asif Arefin, MohammadThe 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.Article Citation - WoS: 35Citation - Scopus: 42A 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; Arqub, Omar AbuThe 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 UniversityArticle Citation - WoS: 41Citation - Scopus: 47New 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. AshikIn 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.Article Citation - WoS: 28Citation - Scopus: 29Solitons 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, DumitruThe 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.Article Citation - WoS: 38Citation - Scopus: 45Protracted 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, HassanIn 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.Article Citation - WoS: 35Citation - Scopus: 41Physically 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; Kumar Barman, HemontaThe 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.Article Citation - WoS: 53Citation - Scopus: 72On 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.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/).Article Citation - WoS: 91Citation - Scopus: 98Novel 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, ChoonkilThis 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.Article Citation - WoS: 32Citation - Scopus: 35A Variety of Novel Exact Solutions for Different Models With the Conformable Derivative in Shallow Water(Frontiers Media Sa, 2020) Kaplan, Melike; Haque, Md. Rabiul; Osman, M. S.; Baleanu, Dumitru; Kumar, DipankarFor 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.