WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Author: search.filters.author.Inc, MustafaPublisher: search.filters.publisher.Springer

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Now showing 1 - 9 of 9
  • Article
    Citation - WoS: 23
    Citation - Scopus: 23
    The Generalized Sasa-Satsuma Equation and Its Optical Solitons
    (Springer, 2022) Hosseini, K.; Sadri, K.; Salahshour, S.; Baleanu, D.; Mirzazadeh, M.; Inc, Mustafa
    The principal goal of the presented paper is to investigate the dynamics of optical solitons for the generalized Sasa-Satsuma (GSS) equation describing the propagation of the femtosecond pulses in the systems of optical fiber transmission. More precisely, the governing model, which is a generalized version of the classical Sasa-Satsuma equation, is firstly reduced in a one-dimensional real regime through a specific transformation; then, its bright and dark optical solitons are established using the modified Kudryashov (MK) method. The changes in the amplitude of the bright and dark solitons are analyzed as a case study for various classes of free parameters. Considerable changes are observed in the optical solitons amplitude from the results presented in the current study.
  • Article
    Citation - WoS: 2
    Citation - Scopus: 3
    On Some Novel Optical Solitons To the Cubic-Quintic Nonlinear Helmholtz Model
    (Springer, 2022) Inc, Mustafa; Tariq, Kalim U.; Tchier, Fairouz; Ilyas, Hamza; Baleanu, Dumitru; Khater, Mostafa M. A.
    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 Schrodinger 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.
  • Article
    Citation - WoS: 47
    Citation - Scopus: 52
    A Delayed Plant Disease Model With Caputo Fractional Derivatives
    (Springer, 2022) Baleanu, Dumitru; Erturk, Vedat Suat; Inc, Mustafa; Govindaraj, V; Kumar, Pushpendra
    We analyze a time-delay Caputo-type fractional mathematical model containing the infection rate of Beddington-DeAngelis functional response to study the structure of a vector-borne plant epidemic. We prove the unique global solution existence for the given delay mathematical model by using fixed point results. We use the Adams-Bashforth-Moulton P-C algorithm for solving the given dynamical model. We give a number of graphical interpretations of the proposed solution. A number of novel results are demonstrated from the given practical and theoretical observations. By using 3-D plots we observe the variations in the flatness of our plots when the fractional order varies. The role of time delay on the proposed plant disease dynamics and the effects of infection rate in the population of susceptible and infectious classes are investigated. The main motivation of this research study is examining the dynamics of the vector-borne epidemic in the sense of fractional derivatives under memory effects. This study is an example of how the fractional derivatives are useful in plant epidemiology. The application of Caputo derivative with equal dimensionality includes the memory in the model, which is the main novelty of this study.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 26
    Boundary Value Problem for Nonlinear Fractional Differential Equations of Variable Order Via Kuratowski Mnc Technique
    (Springer, 2021) Baleanu, Dumitru; Souid, Mohammed Said; Hakem, Ali; Inc, Mustafa; Benkerrouche, Amar; Said Souid, Mohammed
    In the present research study, for a given multiterm boundary value problem (BVP) involving the Riemann-Liouville fractional differential equation of variable order, the existence properties are analyzed. To achieve this aim, we firstly investigate some specifications of this kind of variable-order operators, and then we derive the required criteria to confirm the existence of solution and study the stability of the obtained solution in the sense of Ulam-Hyers-Rassias (UHR). All results in this study are established with the help of the Darbo's fixed point theorem (DFPT) combined with Kuratowski measure of noncompactness (KMNC). We construct an example to illustrate the validity of our observed results.
  • Article
    Citation - WoS: 5
    Citation - Scopus: 5
    On Exact Special Solutions for the Stochastic Regularized Long Wave-Burgers Equation
    (Springer, 2020) Alshomrani, Ali S.; Inc, Mustafa; Baleanu, Dumitru; Korpinar, Zeliha
    In this paper, we will analyze the Regularized Long Wave-Burgers equation with conformable derivative (cd). Some white noise functional solutions for this equation are obtained by using white noise analysis, Hermite transforms, and the modified sub-equation method. These solutions include exact stochastic trigonometric functions, hyperbolic functions solutions and wave solutions. This study emphasizes that the modified fractional sub-equation method is sufficient to solve the stochastic nonlinear equations in mathematical physics.
  • Article
    Citation - WoS: 51
    Citation - Scopus: 61
    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.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 19
    Fractional Optical Solitons for the Conformable Space-Time Nonlinear Schrodinger Equation With Kerr Law Nonlinearity
    (Springer, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
    In this work, we obtain new soliton solutions for the conformable space-time nonlinear Schrodinger equation (CSTNLSE) with Kerr law nonlinearity. Two integration schemes which are projective Ricatti and extended Jacobi elliptic function methods are applied to reach such solutions. The constraints conditions for the existence of soliton solutions are reported. Numerical simulations for some of the obtained solutions are presented.
  • Article
    Citation - WoS: 66
    Citation - Scopus: 63
    Soliton Solutions and Stability Analysis for Some Conformable Nonlinear Partial Differential Equations in Mathematical Physics
    (Springer, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
    This research presents soliton solutions and stability analysis to some conformable nonlinear partial differential equations (CNPDEs). The CNPDEs equations in this paper are conformable Cahn-Allen and conformable Zoomeron equations. The powerful sine-Gordon method is used to carry out the soliton solutions for these equations. The aspects of stability analysis for the considered equations is investigated using the linear stability technique. The sine-Gordon method proves to be efficient and effective for the extraction of soliton solutions for different types of CNPDEs.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 31
    Soliton Structures To Some Time-Fractional Nonlinear Differential Equations With Conformable Derivative
    (Springer, 2018) Yusuf, Abdullahi; Aliyu, Aliyu Isa; Baleanu, Dumitru; Inc, Mustafa
    This research presents new soliton structures to some time-fractional nonlinear differential equations (TFNDEs) with conformable derivative. The powerful Ricatti-Bernoulli (RB) sub-ODE method is used to carry out the soliton solutions. Some of the obtained solutions include trigonometric, periodic wave and hyperbolic solutions. The constraint conditions for the existence of solitons are also presented. The RB sub-ODE method proves to be efficient and effective for the extraction of soliton structures for different types of TFNDEs. Some interesting figures for the numerical simulation of the obtained results are presented.