Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Baleanu, D.Publisher: search.filters.publisher.Springer

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Now showing 1 - 10 of 37
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Fractional Systems With Multi-Parameters Fractional Derivatives
    (Springer, 2025) Muslih, S.I.; Agrawal, O.P.; Baleanu, D.
    Recently, a generalization of fractional variational formulations in terms of multiparameter fractional derivatives was introduced by Agrawal and Muslih. This treatment can be used to obtain the Lagrangian and Hamiltonian equations of motion. In this paper, we also extend our work to introduce the generalization of the formulation for constrained mechanical systems containing multi-parameter fractional derivatives. Three examples for regular and constrained fractional systems are analyzed. © The Author(s) 2025.
  • Book Part
    A New Operator Approach for Solving Time-Fractional Nonlinear Burgess Equation
    (Springer, 2025) Arfaoui, H.; Kharrat, M.; Mecheri, H.; Baleanu, D.
    The introduction of fractional derivatives into the cancer treatment model continues to be improved with current cancer treatment. In this work, we define a new time-fractional nonlinear Burgess equation in order to model the brain tumor growth under treatment. The new mathematical model is in agreement with the clinical data proposed by Stupp et al. (2005). The numerical processing of this model is based on the splitting method which makes it possible to avoid and relax several numerical problems. The numerical results obtained are very satisfactory and excellent. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.
  • Article
    Citation - Scopus: 4
    Ion-Acoustic Solitons in Magnetized Plasma Under Weak Relativistic Effects on the Electrons
    (Springer, 2023) Madhukalya, B.; Das, R.; Hosseini, K.; Baleanu, D.; Salahshour, S.
    Investigating ion-acoustic disturbances in a magnetized plasma, consisting of relativistic electrons and non-thermal ions, entails a comprehensive study into the nonlinear wave structure. By condensing the fundamental set of fluid equations for the flow variables, a singular equation known as the Sagdeev potential equation is derived using the pseudopotential approach. In this investigation of the magnetized relativistic plasma, we have observed only dip (rarefactive) (N< 1) soliton under both subsonic (M< 1) and supersonic (M> 1) conditions. The occurrence of the soliton depends on the wave velocities in different propagation directions. The magnitude of amplitudes of the relativistic solitons is higher for higher Mach number (M> 1) irrespective of the wave’s propagation direction. Furthermore, the magnitude of amplitudes of the solitary wave is seen to increase near the direction of the magnetic field. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.
  • Book Part
    Citation - Scopus: 7
    Fractional Chebyshev Kernel Functions: Theory and Application
    (Springer, 2023) Hadian Rasanan, A.H.; Nedaei Janbesaraei, S.; Baleanu, D.
    Orthogonal functions have many useful properties and can be used for different purposes in machine learning. One of the main applications of the orthogonal functions is producing powerful kernel functions for the support vector machine algorithm. Maybe the simplest orthogonal function that can be used for producing kernel functions is the Chebyshev polynomials. In this chapter, after reviewing some essential properties of Chebyshev polynomials and fractional Chebyshev functions, various Chebyshev kernel functions are presented, and fractional Chebyshev kernel functions are introduced. Finally, the performance of the various Chebyshev kernel functions is illustrated on two sample datasets. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2023.
  • Article
    Citation - Scopus: 10
    Solving System of Fractional Differential Equations Via Vieta-Lucas Operational Matrix Method
    (Springer, 2024) Aeri, S.; Bala, A.; Kumar, R.; Baleanu, D.; Chaudhary, R.
    Vieta-Lucas polynomials (VLPs) belong to the class of weighted orthogonal polynomials, which can be used to effectively handle various natural and engineered problems. The classical fractional derivative due to Caputo is used to write the emerging operational matrices. These matrices are developed and evaluated by using the properties of VLPs. The residuated functions are mapped to zero by the tools of the Tau algorithm. Convergence and error analysis are thoroughly explored. Test examples for a fractional system of differential equations are borrowed from literature. The theoretical and simulated exercise on these examples authenticate the relevance of this scheme. Here, novel inclusion of Vieta-Lucas polynomials has been ensured in combination with the Tau approach. The operational matrix approach which provides extensive information about the fractional derivatives of different terms of Vieta-Lucas polynomial expansion, is ensured to operate to reduce the problem into an algebraic setup. The novelty is further enhanced by comparing the present scheme with the fourth-order Runge–Kutta method. © 2023, The Author(s), under exclusive licence to Springer Nature India Private Limited.
  • Book Part
    Citation - Scopus: 3
    Fractional Gegenbauer Kernel Functions: Theory and Application
    (Springer, 2023) Azmoon, A.; Baleanu, D.; Nedaei Janbesaraei, S.
    Because of the usage of many functions as a kernel, the support vector machine method has demonstrated remarkable versatility in tackling numerous machine learning issues. Gegenbauer polynomials, like the Chebyshev and Legender polynomials which are introduced in previous chapters, are among the most commonly utilized orthogonal polynomials that have produced outstanding results in the support vector machine method. In this chapter, some essential properties of Gegenbauer and fractional Gegenbauer functions are presented and reviewed, followed by the kernels of these functions, which are introduced and validated. Finally, the performance of these functions in addressing two issues (two example datasets) is evaluated. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd 2023.
  • 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: 12
    Citation - Scopus: 13
    Optical Solitons To the Ginzburg-Landau Equation Including the Parabolic Nonlinearity
    (Springer, 2022) Hosseini, K.; Mirzazadeh, M.; Akinyemi, L.; Baleanu, D.; Salahshour, S.
    The major goal of the present paper is to construct optical solitons of the Ginzburg-Landau equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors' knowledge, the results reported in the current study, classified as bright and kink solitons, have a significant role in completing studies on the Ginzburg-Landau equation including the parabolic nonlinearity.
  • Article
    Citation - WoS: 51
    Citation - Scopus: 56
    Optical Solitons of a High-Order Nonlinear Schrodinger Equation Involving Nonlinear Dispersions and Kerr Effect
    (Springer, 2022) Baleanu, D.; Salahshour, S.; Akinyemi, L.; Hosseini, K.; Mirzazadeh, M.
    The main aim of this paper is to conduct a detailed study on a high-order nonlinear Schrodinger (HONLS) equation involving nonlinear dispersions and the Kerr effect. More precisely, after reducing the governing model describing ultra-short pulses in optical fibers in a one-dimensional domain, its optical solitons including the bright and dark solitons are derived through the modified Kudryashov (MK) method. The dynamical behavior of the bright and dark solitons is formally investigated for different sets of the involved parameters. It is shown that increasing and decreasing nonlinear dispersions lead to significant changes in the amplitude of the bright and dark solitons.
  • Article
    Citation - Scopus: 1
    Numerical Investigation of Ordinary and Partial Differential Equations With Variable Fractional Order by Bernstein Operational Matrix
    (Springer, 2022) Alipour, M.; Babakhani, A.; Baleanu, D.; Taleshian, A.H.
    This research proposes a method to find numerical solutions of the variable-order fractional differential equation. We derived new operational matrix by applying Bernstein polynomials. Then, using this matrix, the method of solving the system of variable-order fractional differential equation and variable-order fractional partial differential equation are presented. Various numerical examples of these problems are provided along with the figures and tables. Finally, the accuracy of the proposed method is evaluated. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.