Browsing by Author "Inc, M."

Now showing 1 - 7 of 7

Citation - WoS: 0
Citation - Scopus: 0
Dynamics of solitons of the nonlinear dispersion Drinfel'd-Sokolov system by ansatz method and He's varitional principle
(Soc Mexicana Fisica, 2017) Tchier, F.; Ragoub, L.; Baleanu, D.; Inc, M.; 56389; Matematik
In this article, the exact-special solutions of the nonlinear dispersion Drinferd-Sokolov (shortly D(m, n)) system are analyzed. We use the ansatz approach and the He's variational principle for the mentioned equation. The general formulae for the compactons, solitary patters, solitons and periodic solutions are acquired. These types of solutions are useful and attractive for clarifying some types of nonlinear physical phenomena. These two methods will be used to carry out the integration.
Citation - WoS: 0
Citation - Scopus: 2
New Shape of the Chirped Bright, Dark Optical Solitons and Complex Solutions for (2+1)-Dimensional Ginzburg-Landau Equation and Modulation Instability Analysis
(Soc Mexicana Fisica, 2021) Houwe, A.; Inc, M.; Baleanu, D.; Rezazadeh, H.; Doka, S. Y.; 56389; Matematik
The investigation of the Ginzburg-Landau equation (GLE) has been done to fin out and investigate new chirped bright, dark periodic and singular function solutions. For this purpose, we have used the traveling wave hypothesis and the chirp component. From there it was pointed out the constraint relation to the different arbitrary parameters of the GLE. Thereafter, we have employed the improved sub-ODE method to handle the nonlinear ordinary differential equation (NODE). In the paper, the virtue of the used analytical method has been highlighted via new chirped solitary waves. Besides, to emphasize the confrontation between the nonlinearity and dispersion terms, we have investigated the steady state of the newly obtained results. It has been obtained the Modulation instability (MI) gain spectra under the effect of the power incident and the transverse wave number. In our knowledge, these results are new compared to Refs. [28-34], and are going to be helpful to explain physical phenomena.
Citation - WoS: 0
Nonlinear Self-Adjointness and Nonclassical Solutions of A Population Model With Variable Coefficients
(Amer Scientific Publishers, 2018) Hashemi, M. S.; Inc, M.; Akgul, A.; Baleanu, D.; 56389; Matematik
In this work, the size-structured population model with variable coefficients is considered to construct the exact solutions with nonclassical symmetries in the light of the heir equations. Nonlinear self-adjointness is shown and conservation laws are calculated too. Some scientific theorems have been given in this paper.
Citation - Scopus: 12
On the fractional model of fokker-planck equations with two different operator
(American Institute of Mathematical Sciences, 2020) Korpinar, Z.; Inc, M.; Baleanu, D.; 56389; Matematik
In this paper, the fractional model of Fokker-Planck equations are solved by using Laplace homotopy analysis method (LHAM). LHAM is expressed with a combining of Laplace transform and homotopy methods to obtain a new analytical series solutions of the fractional partial differential equations (FPDEs) in the Caputo-Fabrizio and Liouville-Caputo sense. Here obtained solutions are compared with exact solutions of these equations. The suitability of the method is removed from the plotted graphs. The obtained consequens explain that technique is a power and efficient process in investigation of solutions for fractional model of Fokker-Planck equations. © 2020 the Author(s), licensee AIMS Press.
Citation - Scopus: 7
Some applications of the least squares-residual power series method for fractional generalized long wave equations
(Shanghai Jiaotong University, 2021) Korpinar, Z.; Baleanu, D.; Inc, M.; Almohsen, B.; 56389; Matematik
This article examines a new effective method called the least squares-residual power series method (LS-RPSM) and compares this method with the RPSM. The LS-RPSM assembles the least-squares process with the residual power series method. These techniques are applied to investigate the linear and nonlinear time-fractional regularized long wave equations (TFRLWEs). The RLW models define the shallow water waves in oceans and the internal ion-acoustic waves in plasma. Firstly, we apply the well-known RPSM to acquire approximate solutions. In the next step, the Wronskian determinant is searched in fractional order to show that the functions are linearly independent. After these operations, a system of linear equations is obtained. In the last step, the least-squares algorithm is used to find the necessary coefficients. When this article is examined, it can be said that LS-RPSM is more useful because it requires using fewer terms than the required number of terms when applying the RPSM. Additionally, the experiments show that this method converges better than RPSM. © 2021
Citation - Scopus: 3
Symmetry analysis and some new exact solutions of the newell-whitehead-segel and zeldovich equations
(Cankaya University, 2019) Yusuf, A.; Ghanbari, B.; Qureshi, S.; Inc, M.; Baleanu, D.; 56389; Matematik
The present study offers an overview of Newel-Whitehead-Segel (NWS) and Zeldovich equations (ZEE) equations by Lie symmetry analysis and generalizes rational function methods of exponential function. Some novel complex and real-valued exact solutions for the equations under consideration are presented. Using a new conservation theorem, we construct conservation laws for the ZEE equation. The physical expression for some of the solutions is presented to shed more light on the mechanism of the solutions. © 2019, Cankaya University. All rights reserved.
Citation - WoS: 19
THE FIRST INTEGRAL METHOD FOR THE (3+1)-DIMENSIONAL MODIFIED KORTEWEG-DE VRIES-ZAKHAROV-KUZNETSOV AND HIROTA EQUATIONS
(Editura Acad Romane, 2015) Baleanu, D.; Killic, B.; Ugurlu, Y.; Inc, M.; 56389; Matematik
The first integral method is applied to get the different types of solutions of the (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov and Hirota equations. We obtain envelope, bell shaped, trigonometric, and kink soliton solutions of these nonlinear evolution equations. The applied method is an effective one to obtain different types of solutions of nonlinear partial differential equations.