Browsing by Author "Tchier, Fairouz"

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An Efficient Computational Technique for Fractal Vehicular Traffic Flow
(MDPI, 2018) Baleanu, Dumitru; Tchier, Fairouz; Singh, Jagdev; Baleanu, Dumitru; 56389
In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.
Anti-Synchronization of Chaotic Systems Using A Fractional Conformable Derivative With Power Law
(John Wiley and Sons LTD., 2020) Baleanu, Dumitru; Gomez Aguilar, Jose Francisco; Baleanu, Dumitru; Tchier, Fairouz; Ragoub, Lakhdar; 56389
In this paper, we propose a new numerical method based on two-step Lagrange polynomial interpolation to get numerical simulations and adaptive anti-synchronization schemes for two fractional conformable attractors of variable order. It was considered the fractional conformable derivative in Liouville-Caputo sense. The novel numerical method was applied to derive new results from the anti-synchronization of the identical uncertain Wang-Sun attractors and three-dimensional chaotic system using fractional conformable sliding mode control. Numerical examples show the effectiveness of the adaptive fractional conformable anti-synchronization schemes for the uncertain chaotic systems considered in this paper.
Certain Results Comprising the Weighted Chebyshev Function Using Pathway Fractional Integrals
(MDPI AG, 2020) Baleanu, Dumitru; Baleanu, Dumitru; Tchier, Fairouz; Purohit, Sunil Dutt; 56389
An analogous version of Chebyshev inequality, associated with the weighted function, has been established using the pathway fractional integral operators. The result is a generalization of the Chebyshev inequality in fractional integral operators. We deduce the left sided Riemann Liouville version and the Laplace version of the same identity. Our main deduction will provide noted results for an appropriate change to the Pathway fractional integral parameter and the degree of the fractional operator.
Chaotic Attractors with Fractional Conformable Derivatives in the Liouville-Caputo Sense and Its Dynamical Behaviors
(MDPI, 2018) Baleanu, Dumitru; Francisco Gomez-Aguilar, Jose; Baleanu, Dumitru; Tchier, Fairouz; 56389
This paper deals with a numerical simulation of fractional conformable attractors of type Rabinovich-Fabrikant, Thomas' cyclically symmetric attractor and Newton-Leipnik. Fractional conformable and beta-conformable derivatives of Liouville-Caputo type are considered to solve the proposed systems. A numerical method based on the Adams-Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors. The results of the new type of fractional conformable and beta-conformable attractors are provided to illustrate the effectiveness of the proposed method.
Dynamics of optical solitons, multipliers and conservation laws to the nonlinear schrodinger equation in (2+1)-dimensions with non-Kerr law nonlinearity
(2019) Baleanu, Dumitru; Tchier, Fairouz; İnç, Mustafa; Yusuf, Abdullah; Baleanu, Dumitru; 56389
This work studies the (2 + 1)-dimensional nonlinear Schrodinger equation which arises in optical fibre. Grey and black optical solitons of the model are reported using a suitable complex envelope ansatz solution. The integration lead to some certain conditions which must be satisfied for the solitons to exist. On applying the Chupin Liu's theorem to the grey and black optical solitons, we construct new sets of combined optical soliton solutions of the model. Moreover, classification of conservation laws (Cls) of the model is implemented using the multipliers approach. This is achieved by constructing a set of first-order multipliers of a system of nonlinear partial differential equations acquired by transforming the model into real and imaginary components are derived, which are subsequently used to construct the Cls.
Dynamics of optical solitons, multipliers and conservation laws to the nonlinear schrodinger equation in (2+1)-dimensions with non-Kerr law nonlinearity
(Taylor&Francis LTD, 2019) Baleanu, Dumitru; Tchier, Fairouz; İnç, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; 56389
This work studies the (2 + 1)-dimensional nonlinear Schrodinger equation which arises in optical fibre. Grey and black optical solitons of the model are reported using a suitable complex envelope ansatz solution. The integration lead to some certain conditions which must be satisfied for the solitons to exist. On applying the Chupin Liu's theorem to the grey and black optical solitons, we construct new sets of combined optical soliton solutions of the model. Moreover, classification of conservation laws (Cls) of the model is implemented using the multipliers approach. This is achieved by constructing a set of first-order multipliers of a system of nonlinear partial differential equations acquired by transforming the model into real and imaginary components are derived, which are subsequently used to construct the Cls.
New approximate analytical technique for the solution of time fractional fluid flow models
(2021) Baleanu, Dumitru; Khan, Hassan; Tchier, Fairouz; Hınçal, Evren; Baleanu, Dumitru; Bin Jebreen, Haifa; 56389
In this note, we broaden the utilization of an efficient computational scheme called the approximate analytical method to obtain the solutions of fractional-order Navier–Stokes model. The approximate analytical solution is obtained within Liouville–Caputo operator. The analytical strategy generates the series form solution, with less computational work and fast convergence rate to the exact solutions. The obtained results have shown a simple and useful procedure to analyze complex problems in related areas of science and technology. © 2021, The Author(s).
On new traveling wave solutions of potential KdV and (3+1)-dimensional Burgers equations
(Int Scientific Research Publications, 2016) Baleanu, Dumitru; İnan, İbrahim E.; Uğurlu, Yavuz; İnç, Mustafa; Baleanu, Dumitru; 56389
This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensional Burgers equation (BE) by the two variables (G'/G, 1/G) expansion method (EM). Obtained soliton solutions are designated in terms of kink, bell-shaped solitary wave, periodic and singular periodic wave solutions. These solutions may be useful and desirable to explain some nonlinear physical phenomena. (C) 2016 All rights reserved.
On new traveling wave solutions of potential KdV and (3+1)-dimensional burgers equations
(2016) Baleanu, Dumitru; Inan, Ibrahim E.; Ugurlu, Yavuz; İnç, Mustafa; Baleanu, Dumitru; 56389
This paper acquires soliton solutions of the potential KdV (PKdV) equation and the (3+1)-dimensional Burgers equation (BE) by the two variables (formula presented) expansion method (EM). Obtained soliton solutions are designated in terms of kink, bell-shaped solitary wave, periodic and singular periodic wave solutions. These solutions may be useful and desirable to explain some nonlinear physical phenomena. © 2016. All rights reserved.
On soliton solutions of the Wu-Zhang system
(De Gruyter Open LTD, 2016) Baleanu, Dumitru; Kılıç, Bülent; Karataş, Esra; Al Qurashi, Maysaa Mohamed; Baleanu, Dumitru; Tchier, Fairouz; 56389
In this paper, the extended tanh and hirota methods are used to construct soliton solutions for the WuZhang (WZ) system. Singular solitary wave, periodic and multi soliton solutions of the WZ system are obtained.
On some novel optical solitons to the cubic–quintic nonlinear Helmholtz model
(2022) Baleanu, Dumitru; Inc, Mustafa; Tariq, Kalim U.; Tchier, Fairouz; Ilyas, Hamza; Baleanu, Dumitru; 56389
The purpose of this study is to employ the Sine–Cosine expansion approach to produce some new sort of soliton solutions for the cubic–quintic nonlinear Helmholtz problem. The nonlinear complex model compensates for backward scattering effects that are overlooked in the more popular nonlinear Schrödinger equation. As a result, a number of novel traveling wave structures have been discovered. We also investigate the stability of solitary wave solutions for the governing model. Furthermore, the modulation instability is discussed by employing the standard linear-stability analysis. The 3D, contour and 2D graphs are visualized for several fascinating exact solutions to comprehend their behaviour.
On the approximate solutions of local fractional differential equations with local fractional operators
(MDPI AG, 2016) Baleanu, Dumitru; Jassim, Hassan Kamil; Tchier, Fairouz; Baleanu, Dumitru
In this paper, we consider the local fractional decomposition method, variational iteration method, and differential transform method for analytic treatment of linear and nonlinear local fractional differential equations, homogeneous or nonhomogeneous. The operators are taken in the local fractional sense. Some examples are given to demonstrate the simplicity and the efficiency of the presented methods.
On the solutions of electrohydrodynamic flow with fractional differential equations by reproducing kernel method
(De Gruyter Open Ltd., 2016) Baleanu, Dumitru; Baleanu, Dumitru; İnç, Mustafa; Tchier, Fairouz; 117928; 60693
In this manuscript we investigate electrodynamic flow. For several values of the intimate parameters we proved that the approximate solution depends on a reproducing kernel model. Obtained results prove that the reproducing kernel method (RKM) is very effective. We obtain good results without any transformation or discretization. Numerical experiments on test examples show that our proposed schemes are of high accuracy and strongly support the theoretical results.
Particular solutions of the confluent hypergeometric differential equation by using the nabla fractional calculus operator
(MDPI AG, 2016) Baleanu, Dumitru; İnç, Mustafa; Tchier, Fairouz; Baleanu, Dumitru
In this work; we present a method for solving the second-order linear ordinary differential equation of hypergeometric type. The solutions of this equation are given by the confluent hypergeometric functions (CHFs). Unlike previous studies, we obtain some different new solutions of the equation without using the CHFs. Therefore, we obtain new discrete fractional solutions of the homogeneous and non-homogeneous confluent hypergeometric differential equation (CHE) by using a discrete fractional Nabla calculus operator. Thus, we obtain four different new discrete complex fractional solutions for these equations.
Second-order fast terminal sliding mode control design based on LMI for a class of non-linear uncertain systems and its application to chaotic systems
(Sage Publications LTD, 2017) Baleanu, Dumitru; Baleanu, Dumitru; Tchier, Fairouz; 56389
In this paper, an linear matrix inequalities (LMI)-based second-order fast terminal sliding mode control technique is investigated for the tracking problem of a class of non-linear uncertain systems with matched and mismatched uncertainties. Using the offered approach, a robust chattering-free control scheme is presented to prove the presence of the switching around the sliding surface in the finite time. Based on the Lyapunov stability theorem, the LMI conditions are presented to make the state errors into predictable bounds and the parameters of the controller are obtained in the form of LMI. The control structure is independent of the order of the model. Then, the proposed method is fairly simple and there is no difficulty in the use of this scheme. Simulations on the well-known Genesio's chaotic system and Chua's circuit system are employed to emphasize the success of the suggested scheme. The simulation results on the Genesio's system demonstrate that the offered technique leads to the superior improvement on the control effort and tracking performance.
Solutions of the time fractional reaction-diffusion equations with residual power series method
(Sage Publications Ltd, 2016) Baleanu, Dumitru; İnç, Mustafa; Korpınar, Zeliha S.; Baleanu, Dumitru
In this article, the residual power series method for solving nonlinear time fractional reaction-diffusion equations is introduced. Residual power series algorithm gets Maclaurin expansion of the solution. The algorithm is tested on Fitzhugh-Nagumo and generalized Fisher equations with nonlinearity ranging. The solutions of our equation are computed in the form of rapidly convergent series with easily calculable components using Mathematica software package. Reliability of the method is given by graphical consequences, and series solutions are used to illustrate the solution. The found consequences show that the method is a powerful and efficient method in determination of solution of the time fractional reaction-diffusion equations.
Time Fractional Third-Order Variant Boussinesq System: Symmetry Analysis, Explicit Solutions, Conservation Laws and Numerical Approximations
(Springer Heidelberg, 2018) Baleanu, Dumitru; İnç, Mustafa; Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; 56389
The current work provides comprehensive investigation for the time fractional third-order variant Boussinesq system (TFTOBS) with Riemann-Liouville (RL) derivative. Firstly, we obtain point symmetries, similarity variables, similarity transformation and reduce the governing equation to a special system of ordinary differential equation (ODE) of fractional order. The reduced equation is in the Erdelyi-Kober (EK) sense. Secondly, we solve the reduced system of ODE using the power series (PS) expansion method. The convergence analysis for the power series solution is analyzed and investigated. Thirdly, the new conservation theorem and the generalization of the Noether operators are applied to construct nonlocal conservation laws (CLs) for the TFTOBS. Finally, we use residual power series (RPS) to extract numerical approximation for the governing equations. Interesting figures that explain the physical understanding for both the explicit and approximate solutions are also presented.