Browsing by Author "Inc, Mustafa"

Now showing 1 - 20 of 136

Citation - WoS: 3
Citation - Scopus: 3
Invariant Subspaces, Exact Solutions and Classification of Conservation Laws for a Coupled (1+1)-Dimensional Nonlinear Wu-Zhang Equation
(Iop Publishing Ltd, 2020) Li, Yongjin; Inc, Mustafa; Baleanu, Dumitru; Aliyu, Aliyu Isa
In this work, we apply the invariant subspace method to derive a set of invariant subspaces and solutions of the nonlinear Wu-Zhang equation which describes the dynamic behavior of dispersive long waves in fluid dynamics. The method gives logarithmic and polynomial solutions of the equation. Furthermore, the multipliers approach and new conservation theorem are employed to derive a set of conservation laws of the equation which are to the best of our knowledge reported for the first time in this work. The physical structure of the results is shown by figures of some special solutions in order to give us a better interpretation on the evolution of the solutions.
Citation - WoS: 51
Citation - Scopus: 60
Lie Symmetry Analysis and Explicit Solutions for the Time Fractional Generalized Burgers-Huxley Equation
(Springer, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
In this work, we study the time fractional generalized Burgers-Huxley equation with Riemann-Liouville derivative via Lie symmetry analysis and power series expansion method. We transform the governing equation to nonlinear ordinary differential equation of fractional order using its Lie point symmetries. In the reduced equation, the derivative is in Erdelyi-Kober sense. We apply power series technique to derive explicit solutions for the reduced equation. The convergence of the obtained power series solutions are also derived. Some interesting Figures for the obtained solutions are presented.
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
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: 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
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: 10
Citation - Scopus: 9
Bright, Dark, and Singular Optical Soliton Solutions for Perturbed Gerdjikov-Ivanov Equation
(Vinca inst Nuclear Sci, 2021) Inc, Mustafa; Baleanu, Dumitru; Kumar, Sunil; Ulutas, Esma
This study consider Gerdjikov-Ivanov equation where the perturbation terms appear with full non-linearity. The Jacobi elliptic function ansatz method is implemented to obtain exact solutions of this equation that models pulse dynamics in optical fibers. It is retrieved some bright, dark optical and singular solitons profile in the limiting cases of the Jacobi elliptic functions. The constraint conditions depending on the parameters for the existence of solitons are also presented.
Citation - WoS: 18
Citation - Scopus: 17
Optical Solitons for the Kundu-Eckhaus Equation With Time Dependent Coefficient
(Elsevier Gmbh, Urban & Fischer verlag, 2018) Baleanu, Dumitru; Inc, Mustafa
The first integral method (FIM) is applied to get the different type optical solitons of Kundu-Eckhaus equation (KE). A class of optical solitons of this equation is presented, and some of which are acquired for the first time. Constraint conditions guarantees existence of these solitons. It is illustrated that FIM is very effective method to reach the various type of the soliton solutions. (C) 2018 Elsevier GmbH. All rights reserved.
Citation - WoS: 26
Citation - Scopus: 17
The First Integral Method for Wu-Zhang Nonlinear System With Time-Dependent Coefficients
(Editura Acad Romane, 2015) Baleanu, Dumitru; Baleanu, Dumitru; Kilic, Bulent; Inc, Mustafa; Matematik
The first integral method is used to construct traveling wave solutions of Wu-Zhang nonlinear dynamical system with time-dependent coefficients. We obtained different types of exact solutions by using two types of variable transformations. The method is an effective tool to construct the different types.of exact solutions of nonlinear partial differential equations having real world applications.
Citation - WoS: 102
Citation - Scopus: 106
Time-Fractional Cahn-Allen and Time-Fractional Klein-Gordon Equations: Lie Symmetry Analysis, Explicit Solutions and Convergence Analysis
(Elsevier Science Bv, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
This research analyzes the symmetry analysis, explicit solutions and convergence analysis to the time fractional Cahn-Allen (CA) and time-fractional Klein-Gordon (KG) equations with Riemann-Liouville (RL) derivative. The time fractional CA and time fractional KG are reduced to respective nonlinear ordinary differential equation of fractional order. We solve the reduced fractional ODEs using an explicit power series method. The convergence analysis for the obtained explicit solutions are investigated. Some figures for the obtained explicit solutions are also presented. (C) 2017 Elsevier B.V. All rights reserved.
Citation - WoS: 51
Citation - Scopus: 56
Optical Solitons for Complex Ginzburg-Landau Model in Nonlinear Optics
(Elsevier Gmbh, Urban & Fischer verlag, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
This paper studies the complex Ginzburg-Landau equation (CGLE) which models soliton propagation in the presence of detuning factor in nonlinear optics. Dark, bright, dark-singular and a new dark-bright optical soliton solutions to the model are derived using the sine-Gordon equation method (SGEM). Singular soliton solutions are also celebrated. The model is studied with Kerr law, quadratic-cubic law and parabolic laws nonlinear fibers. It is hoped that the results reported in this paper can enrich the nonlinear dynamical behaviors of the CGLE. (C) 2017 Elsevier GmbH. All rights reserved.
Citation - WoS: 46
Citation - Scopus: 49
Optical Solitons To the Resonance Nonlinear Schrodinger Equation by Sine-Gordon Equation Method
(Academic Press Ltd- Elsevier Science Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
In this paper, we examined the optical solitons to the resonant nonlinear Schrodinger equation (R-NLSE) which describes the propagation of solitons through optical fibers. Three types of nonlinear media fibers are studied. They are; quadratic-cubic law, Kerr law and parabolic law. Dark, bright, dark-bright or combined optical and singular soliton solutions are derived using the sine-Gordon equation method (SGEM). The constraint conditions that naturally fall out of the solution structure which guarantee the existence of these solitons are also reported. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 1
An Analysis of Analytic and Approximate Solutions of the Nonlinear Foam-Drainage Equation and Its Applications
(Amer Scientific Publishers, 2018) Inc, Mustafa; Yusuf, Abdullahi; Baleanu, Dumitru; Aliyu, Aliyu Isa
In this study, the modified Kudryashov and Riccati-Bernoulli (sub-ODE) methods are applied to construct some analytical solutions of the nonlinear Foam-drainage equation which plays an important part in the formation and evolution of liquid foams. Kink type, singular and logarithmic function solutions are obtained. Then, the residual power series method (RPSM) is used to analyze the numerical behavior of the equation by considering all the exact solutions. We observed that the modified Kudryashov and Riccati Bernoulli sub-ODE methods are powerful techniques for finding the exact solutions to various nonlinear models. Also, the RPSM is efficient for examining numerical behavior of nonlinear models. Some interesting figures are shown to show the reliability of the methods.
Citation - WoS: 32
Citation - Scopus: 35
Complexiton and Solitary Wave Solutions of the Coupled Nonlinear Maccaris System Using Two Integration Schemes
(World Scientific Publ Co Pte Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Nuray, Elif; Inc, Mustafa
In this paper, we consider a coupled nonlinear Maccaris system (CNMS) which describes the motion of isolated waves localized in a small part of space. There are some integration tools that are adopted to retrieve the solitary wave solutions. They are the modified F-Expansion and the generalized projective Riccati equation methods. Topological, non-topological, complexiton, singular and trigonometric function solutions are derived. A comparison between the results in this paper and the well-known results in the literature is also given. The derived structures of the obtained solutions offer a rich platform to study the nonlinear CNMS. Numerical simulation of the obtained solutions are presented with interesting figures showing the physical meaning of the solutions.
Citation - WoS: 11
Citation - Scopus: 13
The Deterministic and Stochastic Solutions of the Schrodinger Equation With Time Conformable Derivative in Birefrigent Fibers
(Amer inst Mathematical Sciences-aims, 2020) Inc, Mustafa; Alshomrani, Ali S.; Baleanu, Dumitru; Korpinar, Zeliha
In this manuscript, the deterministic and stochastic nonlinear Schrodinger equation with time conformable derivative is analysed in birefrigent fibers. Hermite transforms, white noise analysis and the modified fractional sub-equation method are used to obtain white noise functional solutions for this equation. These solutions consists of exact stochastic hyperbolic functions, trigonometric functions and wave solutions.
Citation - WoS: 4
Citation - Scopus: 4
Comparison Between the Thermoelectric Properties of New Materials: the Alloy of Iron, Vanadium, Tungsten, and Aluminum (Fe2v0.8w0.2al) Against an Oxide Such as Naco2o4
(Elsevier Gmbh, 2021) Kaid, Noureddine; Ameur, Houari; Inc, Mustafa; Baleanu, Dumitru; Menni, Younes; Lorenzini, Giulio; Sifi, Ibtissem
An analysis of the thermoelectric characteristics of certain recently discovered materials is carried out in this investigation. The alloy of iron, vanadium, tungsten, and aluminum (Fe2V0.8W0.2Al) applied to a silicon crystal is compared to new inorganic thermoelectric materials, which are mosly oxides like NaCO2O4. For both materials, the thermoelectric effects, Seebeck effect, Peltier effect, Thomson effect, and Kelvin relations are described. The cooling rate's influence on the energy balance is also assessed. The traditional thermoelectric materials provided are mostly made up of toxic, rare and/or expensive elements, which makes large-scale thermoelectric generator integration difficult. In recent decades, research has shifted toward the development of novel materials with a better price-to-performance ratio. Despite a low conversion yield, the family of oxides offers significant benefits in this respect, which are particularly evident at high temperatures. The findings of our study indicated that Fe2V0.8W0.2 applied to a silicon crystal has good thermoelectric characteristics. A sufficient merit factor was found in the new substance under investigation.
Citation - WoS: 40
Citation - Scopus: 42
Theory and Application for the Time Fractional Gardner Equation With Mittag-Leffler Kernel
(Taylor & Francis Ltd, 2019) Inc, Mustafa; Baleanu, Dumitru; Bayram, Mustafa; Korpinar, Zeliha
In this work, the time fractional Gardner equation is presented as a new fractional model for Atangana-Baleanu fractional derivative with Mittag-Leffler kernel. The approximate consequences are analysed by applying a recurrent process. The existence and uniqueness of solution for this system is discussed. To explain the effects of several parameters and variables on the movement, the approximate results are shown in graphics and tables.
Citation - WoS: 1
Citation - Scopus: 1
New Approach for Propagated Light With Optical Solitons by Optical Fiber in Pseudohyperbolic Space H0²
(Wiley, 2023) Korpinar, Talat; Korpinar, Zeliha; Baleanu, Dumitru; Cem Demirkol, Ridvan; Inc, Mustafa
In this paper, a new evolution of polarized light ray by optical fiber in the pseudohyperbolic space H-0(2) is examined. Firstly, the characterization of the parallel transportation law associated with the geometric pseudohyperbolic phase of the light ray is given. Later, a principle nature of electric and magnetic field along with the light ray in the pseudohyperbolic space H-0(2) is defined by the geometric invariants. Finally, optical solutions of nonlinear pseudohyperbolic Schrodinger's equations governing the propagation of electromagnetic fields are successfully derived by using the traveling wave hypothesis approach.
Citation - WoS: 24
Citation - Scopus: 26
Conservation Laws, Soliton-Like and Stability Analysis for the Time Fractional Dispersive Long-Wave Equation
(Springeropen, 2018) Inc, Mustafa; Aliyu, Aliyu Isa; Baleanu, Dumitru; Yusuf, Abdullahi
In this manuscript we investigate the time fractional dispersive long wave equation (DLWE) and its corresponding integer order DLWE. The symmetry properties and reductions are derived. We construct the conservation laws (Cls) with Riemann-Liouville (RL) for the time fractional DLWE via a new conservation theorem. The conformable derivative is employed to establish soliton-like solutions for the governing equation by using the generalized projective method (GPM). Moreover, the Cls via the multiplier technique and the stability analysis via the concept of linear stability analysis for the integer order DLWE are established. Some graphical features are presented to explain the physical mechanism of the solutions.
Citation - WoS: 2
Citation - Scopus: 3
On New Traveling Wave Solutions of Potential Kdv and (3+1)-Dimensional Burgers Equations
(int Scientific Research Publications, 2016) Inan, Ibrahim E.; Ugurlu, Yavuz; Inc, Mustafa; Baleanu, Dumitru; Tchiera, Fairouz
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.
Citation - WoS: 40
Citation - Scopus: 48
Dispersive Optical Solitons and Modulation Instability Analysis of Schrodinger-Hirota Equation With Spatio-Temporal Dispersion and Kerr Law Nonlinearity
(Academic Press Ltd- Elsevier Science Ltd, 2018) Aliyu, Aliyu Isa; Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa
This paper obtains the dark, bright, dark-bright or combined optical and singular solitons to the perturbed nonlinear Schrodinger-Hirota equation (SHE) with spatio-temporal dispersion (STD) and Kerr law nonlinearity in optical fibers. The integration algorithm is the Sine-Gordon equation method (SGEM). Furthermore, the modulation instability analysis (MI) of the equation is studied based on the standard linear-stability analysis and the MI gain spectrum is got. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 1
Optical Solitary Wave Solutions for the Conformable Perturbed Nonlinear Schrodinger Equation With Power Law Nonlinearity
(Amer Scientific Publishers, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Gulsen, Selahattin; Baleanu, Dumitru; Inc, Mustafa
In this study, we apply three integration schemes to extract optical soliton solutions for the conformable perturbed nonlinear Schrodinger equation (CPNLSE) with power law nonlinearity (PLN). The integration schemes that are used to carry out such solutions are Sine-Cosine (SC), generalized tanh (GT), and Ricatti-Bernoulli (RB) sub-ODE methods. The constraints conditions for the existence of the solutions are reported. The solutions are obtained using newly proposed fractional derivative called conformable derivative. Numerical simulations of some of the obtained solutions are also illustrated.