Browsing by Author "Rezazadeh, H."

Now showing 1 - 5 of 5

Citation - Scopus: 12
New Exact Solutions of Kolmogorov Petrovskii Piskunov Equation, Fitzhugh Nagumo Equation, and Newell-Whitehead Equation
(Hindawi Limited, 2020) Javeed, S.; Baleanu, D.; Riaz, S.; Rezazadeh, H.; Chu, Y.-M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This work presents the new exact solutions of nonlinear partial differential equations (PDEs). The solutions are acquired by using an effectual approach, the first integral method (FIM). The suggested technique is implemented to obtain the solutions of space-time Kolmogorov Petrovskii Piskunov (KPP) equation and its derived equations, namely, Fitzhugh Nagumo (FHN) equation and Newell-Whitehead (NW) equation. The considered models are significant in biology. The KPP equation describes genetic model for spread of dominant gene through population. The FHN equation is imperative in the study of intercellular trigger waves. Similarly, the NW equation is applied for chemical reactions, Faraday instability, and Rayleigh-Benard convection. The proposed technique FIM can be applied to find the exact solutions of PDEs. © 2020 Yu-Ming Chu et al.
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) Inc, M.; Baleanu, D.; Rezazadeh, H.; Doka, S. Y.; Houwe, A.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
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 - Scopus: 2
A Robust Technique Based Solution of Time-Fractional Seventh-Order Sawada-Kotera and Lax's Kdv Equations
(World Scientific, 2021) Chakraverty, S.; Baleanu, D.; Adel, W.; Rezazadeh, H.; Jena, R.M.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
In this paper, the fractional reduced differential transform method (FRDTM) is used to obtain the series solution of time-fractional seventh-order Sawada-Kotera (SSK) and Lax's KdV (LKdV) equations under initial conditions (ICs). Here, the fractional derivatives are considered in the Caputo sense. The results obtained are contrasted with other previous techniques for a specific case, α = 1 revealing that the presented solutions agree with the existing solutions. Further, convergence analysis of the present results with an increasing number of terms of the solution and absolute error has also been studied. The behavior of the FRDTM solution and the effects on different values α are illustrated graphically. Also, CPU-time taken to obtain the solutions of the title problems using FRDTM has been demonstrated. © 2021 World Scientific Publishing Company.
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.
Citation - WoS: 38
Citation - Scopus: 44
Traveling Wave With Beta Derivative Spatial-Temporal Evolution for Describing the Nonlinear Directional Couplers With Metamaterials Via Two Distinct Methods
(Elsevier, 2021) Hafez, M. G.; Hammouch, Z.; Rezazadeh, H.; Baleanu, D.; Uddin, M. F.; 56389; 02.02. Matematik; 02. Fen-Edebiyat Fakültesi; 01. Çankaya Üniversitesi
This work is reported the analytical solutions for describing the nonlinear directional couplers with metamaterials by including spatial-temporal fractional beta derivative evolution. The auxiliary ordinary differential equation method and the generalized Riccati method with the properties of beta derivative are implemented to secure such solutions. The solutions are obtained in the new forms by involving of some useful mathematical functions. The constraint conditions among the traveling wave parameters are evaluated. Some of the obtained solutions are presented graphically to illustrate the effectiveness of beta derivative parameter and mathematical techniques. It is investigated that the amplitudes of soliton are increased with the increase of fractional beta derivative parameter. The obtained results would be very useful to examine and understand the physical issues in nonlinear optics, especially in twin-core couplers with optical metamaterials. (C) 2020 The Authors. Published by Elsevier B.V. on behalf of Faculty of Engineering, Alexandria University.