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, DumitruPublisher: search.filters.publisher.Asme

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Now showing 1 - 10 of 24
  • Article
    From Eikonal To Antieikonal Approximations: Competition of Scales in the Framework of Schrodinger and Classical Wave Equation
    (Asme, 2022) Pilar Velasco, M.; Baleanu, Dumitru; Luis Vazquez-Poletti, J.; Jimenez, Salvador; Vazquez, Luis; Vázquez-Poletti, J. Luis; Velasco, M. Pilar
    We present a description of certain limits associated with the Schrodinger equation, the classical wave equation, and Maxwell equations. Such limits are mainly characterized by the competition of two fundamental scales. More precisely: (1) The competition of an exploratory wavelength and the scale of fluctuations is associated with the media where the propagation takes place. From that, the universal behaviors arise eikonal and anti-eikonal. (2) In the context above, it is specially relevant and promising the study of propagation of electromagnetic waves in a media with a self-similar structure, like a fractal one. These systems offer the suggestive scenario where the eikonal and anti-eikonal behaviors are simultaneous. This kind of study requires large and massive computations that are mainly possible in the framework of the cloud computing. Recently, we started to carry out this task. (3) Finally and as a collateral aspect, we analyze the Planck constant in the interval 0 <= h <= infinity.
  • Article
    Citation - WoS: 9
    Citation - Scopus: 9
    Fractional Propagation of Short Light Pulses in Monomode Optical Fibers: Comparison of Beta Derivative and Truncated M-Fractional Derivative
    (Asme, 2022) Jhangeer, Adil; Awrejcewicz, Jan; Baleanu, Dumitru; Tahir, Sana; Riaz, Muhammad Bilal
    This study is dedicated to the computation and analysis of solitonic structures of a nonlinear Sasa-Satsuma equation that comes in handy to understand the propagation of short light pulses in the monomode fiber optics with the aid of beta derivative and truncated M-fractional derivative. We employ a new direct algebraic technique for the nonlinear Sasa-Satsuma equation to derive novel soliton solutions. A variety of soliton solutions are retrieved in trigonometric, hyperbolic, exponential, rational forms. The vast majority of obtained solutions represent the lead of this method on other techniques. The prime advantage of the considered technique over the other techniques is that it provides more diverse solutions with some free parameters. Moreover, the fractional behavior of the obtained solutions is analyzed thoroughly by using two and three-dimensional graphs. This shows that for lower fractional orders, i.e., beta = 0.1, the magnitude of truncated Mfractional derivative is greater whereas for increasing fractional orders, i.e., beta = 0.7 and beta = 0.99, the magnitude remains the same for both definitions except for a phase shift in some spatial domain that eventually vanishes and two curves coincide.
  • Article
    On the Fractional Diffusion Equation Associated With Exponential Source and Operator With Exponential Kernel
    (Asme, 2023) Nguyen, Van Tien; Baleanu, Dumitru; Nguyen, Van Thinh; Nguyen, Anh Tuan
    In this paper, we investigate the well-posedness of mild solutions of the time-fractional diffusion equation with an exponential source function and the Caputo-Fabrizio derivative of a fractional order a is an element of ( 0 , 1 ). Some linear estimates of the solution kernels on Hilbert scale spaces are constructed using a spectrum of the Dirichlet Laplacian. Based on the Banach fixed point theorem, the global existence and uniqueness of the small-data mild solution are approved. This work is considered the first study on the time-fractional diffusion equation with a nonlinear function for all common dimensions of 1, 2, and 3.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 9
    Numerical Simulation for Generalized Time-Fractional Burgers' Equation With Three Distinct Linearization Schemes
    (Asme, 2023) Deswal, Komal; Kumar, Devendra; Baleanu, Dumitru; Chawla, Reetika; Reetika, Chawla
    In the present study, we examined the effectiveness of three linearization approaches for solving the time-fractional generalized Burgers' equation using a modified version of the fractional derivative by adopting the Atangana-Baleanu Caputo derivative. A stability analysis of the linearized time-fractional Burgers' difference equation was also presented. All linearization strategies used to solve the proposed nonlinear problem are unconditionally stable. To support the theory, two numerical examples are considered. Furthermore, numerical results demonstrate the comparison of linearization strategies and manifest the effectiveness of the proposed numerical scheme in three distinct ways.
  • Article
    Citation - WoS: 31
    Citation - Scopus: 40
    New Solutions of the Fractional Differential Equations With Modified Mittag-Leffler Kernel
    (Asme, 2023) Baleanu, Dumitru; Odibat, Zaid
    This paper is concerned with some features of the modified Caputo-type Mittag-Leffler fractional derivative operator and its associated fractional integral operator. Mainly, new types of solutions for fractional differential equations with Mittag-Leffler kernel are generated based on a numerical algorithm developed in this paper. The suggested algorithm is used to describe the solution behavior of models involving modified Caputo-type Mittag-Leffler fractional derivatives. The results described in this paper are expected to be effectively employed in the area of simulating related fractional models.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 15
    Fractional Dynamics and Analysis of Coupled Schrodinger-Kdv Equation With Caputo-Katugampola Type Memory
    (Asme, 2023) Gupta, Arpita; Baleanu, Dumitru; Singh, Jagdev
    Fundamental purpose of the current research article is to analyze the behavior of obtained results of time fractional nonlinear coupled Schrodinger-KdV equation, via implementing an effective analytical technique. In this work, Katugampola fractional derivative in Caputo type is used to model the problem. The coupled Schrodinger-KdV equation describes several kinds of wave propagation in plasma physics, like electromagnetic waves, dust-acoustic waves, and Langmuir waves. The fixed point theorem is used to present the existence and uniuness analysis of obtained solution of the discussed model. Numerical simulation and graphical behavior of the model are presented to show the reliability of the implemented analytical technique. A comparative analysis of exact and obtained approximate solutions is also presented.
  • Article
    Citation - WoS: 5
    The Fractional Linear Systems of Equations Within an Operational Approach
    (Asme, 2013) Saadatmandi, Abbas; Kadem, Abdelouahab; Dehghan, Mehdi; Baleanu, Dumitru
    Fractional calculus is a rapidly going area from both experimental and theoretical points of view. As a result new methods and techniques should be developed in order to deal with new types of fractional differential equations. In this paper the operational matrix of fractional derivative together with the tau method are used to solve the linear systems of fractional differential equations. The results of this method are shown by solving three illustrative examples. By comparing the obtained results with the analytic solutions and with the ones provided by three standard methods for solving the fractional differential equations we conclude that our method gave comparable results.
  • Article
    Citation - WoS: 33
    Citation - Scopus: 39
    An Efficient Technique for Fractional Coupled System Arisen in Magnetothermoelasticity With Rotation Using Mittag-Leffler Kernel
    (Asme, 2021) Prakasha, D. G.; Baleanu, Dumitru; Veeresha, P.
    In this paper, we find the solution for fractional coupled system arisen in magnetothermoelasticity with rotation using q-homotopy analysis transform method ( q-HATM). The proposed technique is graceful amalgamations of Laplace transform technique with q-homotopy analysis scheme, and fractional derivative defined with Mittag-Leffler kernel. The fixed point hypothesis is considered to demonstrate the existence and uniqueness of the obtained solution for the proposed fractional order model. To illustrate the efficiency of the future technique, we analyzed the projected model in terms of fractional order. Moreover, the physical behavior of q-HATM solutions has been captured in terms of plots for different arbitrary order. The attained consequences confirm that the considered algorithm is highly methodical, accurate, very effective, and easy to implement while examining the nature of fractional nonlinear differential equations arisen in the connected areas of science and engineering.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 18
    New Fractional Analytical Study of Three-Dimensional Evolution Equation Equipped With Three Memory Indices
    (Asme, 2019) Alquran, Marwan; Jaradat, Imad; Momani, Shaher; Baleanu, Dumitru; Yousef, Feras
    Herein, analytical solutions of three-dimensional (3D) diffusion, telegraph, and Burgers' models that are equipped with three memory indices are derived by using an innovative fractional generalization of the traditional differential transform method (DTM), namely, the threefold-fractional differential transform method (threefold-FDTM). This extends the applicability of DTM to comprise initial value problems in higher fractal spaces. The obtained solutions are expressed in the form of a (gamma) over bar -fractional power series which is a fractional adaptation of the classical Taylor series in several variables. Furthermore, the projection of these solutions into the integer space corresponds with the solutions of the classical copies for these models. The results detect that the suggested method is easy to implement, accurate, and very efficient in (non)linear fractional models. Thus, research on this trend is worth tracking.
  • Article
    Citation - WoS: 43
    Nonlinear Dynamics of Cattaneo-Christov Heat Flux Model for Third-Grade Power-Law Fluid
    (Asme, 2020) Kumar, Sunil; Cattani, Carlo; Baleanu, Dumitru; Sharma, Bhuvnesh
    A rigorous analysis of coupled nonlinear equations for third-grade viscoelastic power-law non-Newtonian fluid is presented. Initially, the governing partial differential equations for conservation of energy and momentum are transformed to nonlinear coupled ordinary differential equations using exact similarity transformations which are known as Cattaneo-Christov heat flux model for third-grade power-law fluid. The homotopy analysis method (HAM) is utilized to approximate the systematic solutions more precisely with shear-thickening, moderately shear-thinning, and most shear-thinning fluids. The solution depends on various parameters including Prandtl number, power index, and temperature variation coefficient. A systematic analysis of boundary-layer flow demonstrates the impact of these parameters on the velocity and temperature profiles.