WoS İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Baleanu, D.WoS Q: search.filters.wosQuartile.Q1

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Now showing 1 - 10 of 108
  • Article
    Citation - WoS: 5
    On the Solution of a Parabolic PDE Involving a Gas Flow Through a Semi-Infinite Porous Medium
    (Amsterdam, 2021) Pop, Daniel N.; Vrinceanu, N.; Al-Omari, S.; Ouerfelli, N.; Baleanu, D.; Nisar, K. S.
    Taking as start point the parabolic partial differential equation with the respective initial and boundary conditions, the present research focuses onto the flow of a sample of waste-water derived from a standard/conventional dyeing process. In terms of a highly prioritized concern, meaning environment decontamination and protection, in order to remove the dyes from the waste waters, photocatalyses like ZnO or TiO2 nanoparticles were formulated, due to their high surface energy which makes them extremely reactive and attractive. According to the basics of ideal fluid, the key point is the gas flow through an ideal porous pipe consisting of nanoparticles bound one to each other, forming a porous matrix/pipe. The modeling of the gas flow through a porous media is quite valuable because of its importance in investigating the gas-solid processes. The present study is a valid contribution to the existing literature, by developing a nonstandard line method for the partial differential equation, in order to obtain a numerical solution of unsteady flow of gas through nano porous medium. Hence, the physical problem is modeled by a highly nonlinear ordinary differential equation detailed on a semi-finite domain and represents a guidance for several questions originating in the gas flow theory. The findings of this study offered a facile approach to improve an attractive issue related to materials science/chemistry, like synthesis of ZnO or TiO2 nanoparticles forming an ideal nano porous pipe with efficiency in industrial waste waters decontamination.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 3
    Numerical Solution of Space-Time Variable Fractional Order Advection-Dispersion Equation Using Jacobi Spectral Collocation Method
    (Univ Putra Malaysia Press, 2020) Moghadam, Soltanpour A.; Baleanu, Dumitru; Arabameri, M.; Barfeie, M.; Baleanu, D.; Soltanpour Moghadam, A.; Matematik
    This article is aimed at studying computational solution of variable order fractional advection-dispersion equation for one-dimensional and two-dimensional spaces utilizing spectral collocation method. In the considered model, the time derivative is Coimbra fractional derivative and space derivative is a Riemann-Liouville derivative. Jacobi polynomials are applied as basic functions in approximation of the solution. The presented approach is an application of the shifted Jacobi-Gauss collocation (SJ-G-C) and the shifted Jacobi-Gauss-Radau collocation (SJ-GR-C) methods using for discretizing along space and time, respectively. Using the related collocation points, the problem would be changed to an algebraic equation system, which can be tackled applying a computational technique. At the end, several examples in one and two dimensional cases have been solved by introduced approach, it would be shown that the proposed numerical algorithm has considerably higher accuracy in contrast to the existing computational schemes including finite difference approach.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 2
    Unification and Extension of the Factorization Method for Constructing Exactly and Conditionally-Exactly Solvable Potentials. the Case of a Single Potential Generating Function
    (Elsevier, 2022) Nigmatullin, R. R.; Khamzin, A. A.; Baleanu, D.
    The article proposes a new algorithm for applying the factorization method to the problem of calculating the spectrum of exactly and conditionally exactly solvable potentials. The proposed algorithm allows us to unify and extend the capabilities of the factorization method to construct exactly solvable potentials. The new approach is demonstrated by calculating the eigenvalues of exactly solvable potentials constructed using a single function in the form of the Laurent-type polynomial. The algorithm makes it possible to significantly simplify the scheme for calculating the spectrum, parameters of the superpotential, as well as the constrain conditions for the parameters of the potential, in the case of conditionally exactly solvable potentials. It is shown that the shape of the spectrum is determined only by the differential equation, which is satisfied by the potential generating function.
  • 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 - WoS: 50
    Citation - Scopus: 55
    Numerical Analysis of Atangana-Baleanu Fractional Model To Understand the Propagation of a Novel Corona Virus Pandemic
    (Elsevier, 2022) Butt, A. I. K.; Ahmad, W.; Rafiq, M.; Baleanu, D.
    In this manuscript, we formulated a new nonlinear SEIQR fractional order pandemic model for the Corona virus disease (COVID-19) with Atangana-Baleanu derivative. Two main equilibrium points F-0*, F-1* of the proposed model are stated. Threshold parameter R-0 for the model using next generation technique is computed to investigate the future dynamics of the disease. The existence and uniqueness of solution is proved using a fixed point theorem. For the numerical solution of fractional model, we implemented a newly proposed Toufik-Atangana numerical scheme to validate the importance of arbitrary order derivative q and our obtained theoretical results. It is worth mentioning that fractional order derivative provides much deeper information about the complex dynamics of Corona model. Results obtained through the proposed scheme are dynamically consistent and good in agreement with the analytical results. To draw our conclusions, we explore a complete quantitative analysis of the given model for different quarantine levels. It is claimed through numerical simulations that pandemic could be eradicated faster if a human community selfishly adopts mandatory quarantine measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effectiveness of quarantine policy on human population. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
  • Article
    Citation - WoS: 21
    Citation - Scopus: 25
    The (K, S)-Fractional Calculus of K-Mittag Function
    (Springer, 2017) Nisar, K. S.; Rahman, G.; Baleanu, D.; Mubeen, S.; Arshad, M.
    In this paper, we introduce the (k, s)-fractional integral and differential operators involving k-Mittag-Leffler function E-k,rho,beta(delta) (z) as its kernel. Also, we establish various properties of these operators. Further, we consider a number of certain consequences of the main results.
  • Article
    Citation - WoS: 29
    Citation - Scopus: 30
    Monic Chebyshev Pseudospectral Differentiation Matrices for Higher-Order Ivps and Bvps: Applications To Certain Types of Real-Life Problems
    (Springer Heidelberg, 2022) Abdelhakem, M.; Ahmed, A.; Baleanu, D.; El-kady, M.
    We introduce new differentiation matrices based on the pseudospectral collocation method. Monic Chebyshev polynomials (MCPs) were used as trial functions in differentiation matrices (D-matrices). Those matrices have been used to approximate the solutions of higher-order ordinary differential equations (H-ODEs). Two techniques will be used in this work. The first technique is a direct approximation of the H-ODE. While the second technique depends on transforming the H-ODE into a system of lower order ODEs. We discuss the error analysis of these D-matrices in-depth. Also, the approximation and truncation error convergence have been presented to improve the error analysis. Some numerical test functions and examples are illustrated to show the constructed D-matrices' efficiency and accuracy.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 4
    Further Studies on Ordinary Differential Equations Involving the M-Fractional Derivative
    (Amer inst Mathematical Sciences-aims, 2022) Khoshkenar, A.; Ilie, M.; Hosseini, K.; Baleanu, D.; Salahshour, S.; Park, C.; Lee, J. R.
    In the current paper, the power series based on the M-fractional derivative is formally introduced. More peciesely, the Taylor and Maclaurin expansions are generalized for fractional-order differentiable functions in accordance with the M-fractional derivative. Some new definitions, theorems, and corollaries regarding the power series in the M sense are presented and formally proved. Several ordinary differential equations (ODEs) involving the M-fractional derivative are solved to examine the validity of the results presented in the current study.