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Access Right: Closed AccessSubject: search.filters.subject.Atangana-Baleanu Derivative

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  • Book Part
    Strange Chaotic Attractors and Existence Results Via Nonlinear Fractional Order Systems and Fixed Points
    (Springer, 2024) Panda, S.K.; Vijayakumar, V.; Gopinadh, B.S.; Jarad, F.
    An analog of Meir-Keeler’s fixed point result in suprametric space is proved in this paper, and application to strange attractors in the context of the Atangana-Baleanu derivative is discussed. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.
  • Article
    Citation - WoS: 42
    Citation - Scopus: 44
    A Numerical Approach for Solving Fractional Optimal Control Problems With Mittag-Leffler Kernel
    (Sage Publications Ltd, 2022) Ganji, Roghayeh M.; Sayevand, Khosro; Baleanu, Dumitru; Jafari, Hossein
    In this work, we present a numerical approach based on the shifted Legendre polynomials for solving a class of fractional optimal control problems. The derivative is described in the Atangana-Baleanu derivative sense. To solve the problem, operational matrices of AB-fractional integration and multiplication, together with the Lagrange multiplier method for the constrained extremum, are considered. The method reduces the main problem to a system of nonlinear algebraic equations. In this framework by solving the obtained system, the approximate solution is calculated. An error estimate of the numerical solution is also proved for the approximate solution obtained by the proposed method. Finally, some illustrative examples are presented to demonstrate the accuracy and validity of the proposed scheme.
  • Article
    Citation - WoS: 201
    Citation - Scopus: 209
    Analysis of Regularized Long-Wave Equation Associated With a New Fractional Operator With Mittag-Leffler Type Kernel
    (Elsevier, 2018) Singh, Jagdev; Baleanu, Dumitru; Sushila; Kumar, Devendra
    In this work, we aim to present a new fractional extension of regularized long-wave equation. The regularized long-wave equation is a very important mathematical model in physical sciences, which unfolds the nature of shallow water waves and ion acoustic plasma waves. The existence and uniqueness of the solution of the regularized long-wave equation associated with Atangana Baleanu fractional derivative having Mittag-Leffler type kernel is verified by implementing the fixed-point theorem. The numerical results are derived with the help of an iterative algorithm. In order to show the effects of various parameters and variables on the displacement, the numerical results are presented in graphical and tabular form. (C) 2017 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 121
    Citation - Scopus: 138
    New Aspects of Fractional Biswas-Milovic Model With Mittag-Leffler Law
    (Edp Sciences S A, 2019) Kumar, Devendra; Baleanu, Dumitru; Singh, Jagdev
    This article deals with a fractional extension of Biswas-Milovic (BM) model having Kerr and parabolic law nonlinearities. The BM model plays a key role in describing the long-distance optical communications. The fractional homotopy analysis transform technique (FHATM) is applied to examine the BM equation involving Atangana-Baleanu (AB) derivative of fractional order. The FHATM is constructed by using homotopy analysis technique, Laplace transform algorithm and homotopy polynomials. The numerical simulation work is performed with the aid of maple software package. In order to demonstrate the effects of order of AB operator, variables and parameters on the displacement, the results are shown graphically. The outcomes of the present investigation are very encouraging and show that the AB fractional operator is very useful in mathematical modelling of natural phenomena.
  • Article
    Citation - WoS: 177
    Citation - Scopus: 188
    New Results on Existence in the Framework of Atangana-Baleanu Derivative for Fractional Integro-Differential Equations
    (Pergamon-elsevier Science Ltd, 2019) Logeswari, K.; Jarad, Fahd; Ravichandran, C.
    In this article, we consider integro-differential equations involving the recently explored Atangana-Baleanu fractional derivatives which contain the generalized Mittag-Leffler functions in their kernels. Utilizing fixed point techniques, we examine the existence and uniqueness of solutions to such equations in Banach spaces. Moreover, we consider an example and investigate numerical outcomes for various values of the fractional order. Then, we consider the stability of the tackled integro-differential equation in the frame of Ulam. (C) 2019 Elsevier Ltd. All rights reserved.
  • Article
    Citation - WoS: 186
    Citation - Scopus: 211
    On the Analysis of Vibration Equation Involving a Fractional Derivative With Mittag-Leffler Law
    (Wiley, 2020) Singh, Jagdev; Baleanu, Dumitru; Kumar, Devendra
    The present article deals with a fractional extension of the vibration equation for very large membranes with distinct special cases. The fractional derivative is considered in Atangana-Baleanu sense. A numerical algorithm based on homotopic technique is employed to examine the fractional vibration equation. The stability analysis is conducted for the suggested scheme. The maple software package is utilized for numerical simulation. In order to illustrate the effects of space, time, and order of Atangana-Baleanu derivative on the displacement, the outcomes of this study are demonstrated graphically. The results revel that the Atangana-Baleanu fractional derivative is very efficient in describing vibrations in large membranes.