Browsing by Author "Ghanbari, Behzad"

Now showing 1 - 12 of 12

Citation - WoS: 22
Citation - Scopus: 22
Abundant Optical Solitons To the (2+1)-Dimensional Kundu-Mukherjee Equation in Fiber Communication Systems
(Springer, 2023) Baleanu, Dumitru; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The Kundu-Mukherjee-Naskar equation holds significant relevance as a nonlinear model for investigating intricate wave phenomena in fluid and optical systems. This study uncovers new optical soliton solutions for the KMN equation by employing analytical techniques that utilize combined elliptic Jacobian functions. The solutions exhibit mixtures of distinct Jacobian elliptic functions, offering novel insights not explored in prior KMN equation research. Visual representations in the form of 2D ContourPlots elucidate the physical behaviors and properties of these newly discovered solution forms. The utilization of symbolic computations facilitated the analytical derivation of these solutions, offering a deeper understanding of the nonlinear wave dynamics governed by the KMN equation. These employed techniques showcase the potential for future analytical advancements in unraveling the complex soliton landscape of the multifaceted KMN model. The findings provide valuable insights into the intricacies of soliton behavior within this nonlinear system, offering new perspectives for analysis and exploration in areas such as fiber optic communications, ocean waves, and fluid mechanics. Maple symbolic packages have enabled us to derive analytical results.
Citation - WoS: 52
Citation - Scopus: 57
Applications of Two Novel Techniques in Finding Optical Soliton Solutions of Modified Nonlinear Schrodinger Equations
(Elsevier, 2023) Baleanu, Dumitru; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Finding optical soliton solutions to nonlinear partial differential equations has become a popular topic in recent decades. The primary goal of this study is to identify a diverse collection of wave solutions to a generalized version of the nonlinear Schrodinger equation. We investigate two modifications to the generalized exponential rational function method to derive the expected results for this model. The first method is primarily based on using elementary functions such as exponential, trigonometric, and hyperbolic forms, which are commonly used to calculate the results. As for the second method, it is based on applying Jacobi elliptic functions to formulate solutions, whereas the underlying idea is the same as with the first method. As a means of enhancing the reader's understanding of the results, we plot the graphical properties of our solutions. Based on this article's results, it can be concluded that both techniques are easy to follow, and yet very efficient. These integration methods can determine different categories of solutions all in a unified framework. Therefore, it can be concluded from the manuscript that the approaches adopted in the manuscript may be regarded as efficient tools for determining wave solutions of a variety of partial differential equations. Due to the high computational complexity, the main requirement for applying our proposed methods is to employ an efficient computing software. Here, symbolic packages in Wolfram Mathematica have been used to validate the entire results of the paper.
Citation - WoS: 19
Families of Exact Solutions of Biswas-Milovic Equation by an Exponential Rational Function Method
(Tbilisi Centre Math Sci, 2020) Ghanbari, Behzad; Baleanu, Dumitru; Inc, Mustfa; Yusuf, Abdullahi; Baleanu, Dumitru; Bayram, Mustafa; 56389; Matematik; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we introduce generalized exponential rational function method (GERFM) to obtain an exact solutions for the Biswas-Milovic (BM) equation with quadratic-cubic and parabolic nonlinearities. A wide range of closed solutions are acquired. The most important feature of the new method is that it is very effective and simple. The main merits of the proposed is that it gives more general solutions with some free parameters and can be applied to other types of nonlinear partial differential equations.Some interesting Figures for the physical features of some of the obtained solutions are also presented.
Citation - WoS: 66
Citation - Scopus: 74
The Lie Symmetry Analysis and Exact Jacobi Elliptic Solutions for the Kawahara-Kdv Type Equations
(Elsevier, 2021) Kumar, Sachin; Niwas, Monika; Baleanu, Dumitru; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this article, we aim to employ two analytical methods including, the Lie symmetry method and the Jacobi elliptical solutions finder method to acquire exact solitary wave solutions in various forms of (1+1) dimensional Kawahara?KdV type equation and modified Kawahara?KdV type equation. These models are famous models that arise in the modeling of many complex physical phenomena. At the outset, we have generated geometric vector fields and infinitesimal generators of Kawahara?KdV type equations. The (1+1) dimensional Kawahara?KdV type equations reduced into ordinary differential equations (ODEs) using Lie symmetry reductions. Furthermore, numerous exact solitary wave solutions are obtained utilizing the Jacobi elliptical solutions finder method with the help of symbolic computation with Maple. The obtained results are new in the formulation, and more useful to explain complex physical phenomena. The results reveal that these mathematical approaches are straightforward, effective, and powerful methods that can be adopted for solving other nonlinear evolution equations.
Citation - WoS: 170
Citation - Scopus: 179
A New and Efficient Numerical Method for the Fractional Modeling and Optimal Control of Diabetes and Tuberculosis Co-Existence
(Amer inst Physics, 2019) Ghanbari, Behzad; Baleanu, Dumitru; Jajarmi, Amin; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The main objective of this research is to investigate a new fractional mathematical model involving a nonsingular derivative operator to discuss the clinical implications of diabetes and tuberculosis coexistence. The new model involves two distinct populations, diabetics and nondiabetics, while each of them consists of seven tuberculosis states: susceptible, fast and slow latent, actively tuberculosis infection, recovered, fast latent after reinfection, and drug-resistant. The fractional operator is also considered a recently introduced one with Mittag-Leffler nonsingular kernel. The basic properties of the new model including non-negative and bounded solution, invariant region, and equilibrium points are discussed thoroughly. To solve and simulate the proposed model, a new and efficient numerical method is established based on the product-integration rule. Numerical simulations are presented, and some discussions are given from the mathematical and biological viewpoints. Next, an optimal control problem is defined for the new model by introducing four control variables reducing the number of infected individuals. For the control problem, the necessary and sufficient conditions are derived and numerical simulations are given to verify the theoretical analysis.
Citation - WoS: 113
Citation - Scopus: 120
The New Exact Solitary Wave Solutions and Stability Analysis for the (2+1)-Dimensional Zakharov-Kuznetsov Equation
(Pushpa Publishing House, 2019) Yusuf, Abdullahi; Inc, Mustafa; Baleanu, Dumitru; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, a new generalized exponential rational function method is employed to extract new solitary wave solutions for the Zakharov-Kuznetsov equation (ZKE). The ZKE exhibits the behavior of weakly nonlinear ion-acoustic waves in incorporated hot isothermal electrons and cold ions in the presence of a uniform magnetic field. Furthermore, the stability for the governing equations is investigated via the aspect of linear stability analysis. Numerical simulations are made to shed light on the characteristics of the obtained solutions.
Citation - WoS: 67
Citation - Scopus: 79
New Exact Solutions of the Generalized Benjamin-Bona Equation
(Mdpi, 2019) Baleanu, Dumitru; Al Qurashi, Maysaa; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The recently introduced technique, namely the generalized exponential rational function method, is applied to acquire some new exact optical solitons for the generalized Benjamin-Bona-Mahony (GBBM) equation. Appropriately, we obtain many families of solutions for the considered equation. To better understand of the physical features of solutions, some physical interpretations of solutions are also included. We examined the symmetries of obtained solitary waves solutions through figures. It is concluded that our approach is very efficient and powerful for integrating different nonlinear pdes. All symbolic computations are performed in Maple package.
Citation - WoS: 90
Citation - Scopus: 97
New Optical Solutions of the Fractional Gerdjikov-Ivanov Equation With Conformable Derivative
(Frontiers Media Sa, 2020) Baleanu, Dumitru; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
Finding exact analytic solutions to the partial equations is one of the most challenging problems in mathematical physics. Generally speaking, the exact solution to many categories of such equations can not be found. In these cases, the use of numerical and approximate methods is inevitable. Nevertheless, the exact PDE solver methods are always preferred because they present the solution directly without any restrictions to use. This article aims to examine the perturbed Gerdjikov-Ivanov equation in an exact approach point of view. This equation plays a significant role in non-linear fiber optics. It also has many important applications in photonic crystal fibers. To this end, firstly, we obtain some novel optical solutions of the equation via a newly proposed analytical method called generalized exponential rational function method. In order to understand the dynamic behavior of these solutions, several graphs are plotted. To the best of our knowledge, these two techniques have never been tested for the equation in the literature. The findings of this article may have a high significance application while handling the other non-linear PDEs.
Citation - WoS: 37
Citation - Scopus: 41
New Solitary Wave Solutions and Stability Analysis of the Benney-Luke and the Phi-4 Equations in Mathematical Physics
(Amer inst Mathematical Sciences-aims, 2019) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, we present new solitary wave solutions for the Benney-Luke equation (BLE) and Phi-4 equation (PE). The new generalized rational function method (GERFM) is used to reach such solutions. Moreover, the stability for the governing equations is investigated via the aspect of linear stability analysis. It is proved that, both the governing equations are stable. We can also solve other nonlinear system of PDEs which are involve in mathematical physics and many other branches of physical sciences with the help of this new method.
Citation - WoS: 59
Citation - Scopus: 65
New Solutions of Gardner's Equation Using Two Analytical Methods
(Frontiers Media Sa, 2019) Baleanu, Dumitru; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This article introduces and applies new methods to determine the exact solutions of partial differential equations that will increase our understanding of the capabilities of applied models in real-world problems. With these new solutions, we can achieve remarkable advances in science and technology. This is the basic idea in this article. To accurately describe this, some exact solutions to the Gardner's equation are obtained with the help of two new analytical methods including the generalized exponential rational function method and a Jacobi elliptical solution finder method. A set of new exact solutions containing four parameters is reported. The results obtained in this paper are new solutions to this equation that have not been introduced in previous literature. Another advantage of these methods is the determination of the varied solutions involving various classes of functions, such as exponential, trigonometric, and elliptic Jacobian. The three-dimensional diagrams of some of these solutions are plotted with specific values for their existing parameters. By examining these graphs, the behavior of the solution to this equation will be revealed. Mathematica software was used to perform the computations and simulations. The suggested techniques can be used in other real-world models in science and engineering.
Citation - WoS: 77
Citation - Scopus: 86
A Novel Technique To Construct Exact Solutions for Nonlinear Partial Differential Equations
(Springer Heidelberg, 2019) Baleanu, Dumitru; Ghanbari, Behzad; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
The aim of the manuscript is to present a new exact solver of nonlinear partial differential equations. The proposed technique is developed by extending the phi(6)-model expansion method as a known method. The corresponding exact solutions are given in terms of Jacobi elliptic functions. Some new optical solutions of the resonant nonlinear Schrodinger equation are constructed within this newly proposed method. For some specific choices of the modulus of Jacobi elliptic functions, various solutions of the equation are introduced. Some numerical simulations are also included to emphasize that all parameters have major influences for the solitary waves behaviours. The proposed technique is very simple and straightforward, and can be employed to solve other non-linear partial differential equations.
Citation - WoS: 125
Citation - Scopus: 137
Planar System-Masses in an Equilateral Triangle: Numerical Study Within Fractional Calculus
(Tech Science Press, 2020) Ghanbari, Behzad; Asad, Jihad H.; Jajarmi, Amin; Pirouz, Hassan Mohammadi; Baleanu, Dumitru; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this work, a system of three masses on the vertices of equilateral triangle is investigated. This system is known in the literature as a planar system. We first give a description to the system by constructing its classical Lagrangian. Secondly, the classical Euler-Lagrange equations (i.e., the classical equations of motion) are derived. Thirdly, we fractionalize the classical Lagrangian of the system, and as a result, we obtain the fractional Euler-Lagrange equations. As the final step, we give the numerical simulations of the fractional model, a new model which is based on Caputo fractional derivative.