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

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Publisher: search.filters.publisher.ElsevierSubject: search.filters.subject.Caputo Derivative

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Now showing 1 - 5 of 5
  • Article
    Citation - WoS: 41
    Citation - Scopus: 44
    Nonlinear Dynamics and Chaos in Fractional Differential Equations With a New Generalized Caputo Fractional Derivative
    (Elsevier, 2022) Baleanu, Dumitru; Odibat, Zaid
    In this paper, novel systems of fractional differential equations involving a new generalized Caputo fractional derivative were proposed. The complex dynamic behavior of these systems was studied by numerical simulation. Nonlinear dynamics and chaos in hybrid fractional order systems were investigated using a predictor-corrector algorithm. In particular, the effect of the new generalized fractional derivative parameters on the dynamics of the proposed systems was discussed. The rich variation obtained from the characteristics of the studied systems recommends the implementation of the new generalized derivative in fractional calculus applications.
  • Article
    Citation - WoS: 29
    Citation - Scopus: 33
    A New Fractional Derivative Operator With Generalized Cardinal Sine Kernel: Numerical Simulation
    (Elsevier, 2023) Baleanu, Dumitru; Odibat, Zaid
    In this paper, we proposed a new fractional derivative operator in which the generalized cardinal sine function is used as a non-singular analytic kernel. In addition, we provided the corresponding fractional integral operator. We expressed the new fractional derivative and integral operators as sums in terms of the Riemann-Liouville fractional integral operator. Next, we introduced an efficient extension of the new fractional operator that includes integrable singular kernel to overcome the initialization problem for related differential equations. We also proposed a numerical approach for the numerical simulation of IVPs incorporating the proposed extended fractional derivatives. The proposed fractional operators, the developed relations and the presented numerical method are expected to be employed in the field of fractional calculus.(c) 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 37
    Citation - Scopus: 45
    An Effective Computational Method To Deal With a Time-Fractional Nonlinear Water Wave Equation in the Caputo Sense
    (Elsevier, 2021) Ilie, Mousa; Mirzazadeh, Mohammad; Yusuf, Abdullahi; Sulaiman, Tukur Abdulkadir; Baleanu, Dumitru; Salahshour, Soheil; Hosseini, Kamyar
    The authors' concern of the present paper is to conduct a systematic study on a time-fractional nonlinear water wave equation which is an evolutionary version of the Boussinesq system. The study goes on by adopting a new analytical method based on the Laplace transform and the homotopy analysis method to the governing model and obtaining its approximate solutions in the presence of the Caputo fractional derivative. To analyze the influence of the Caputo operator on the dynamical behavior of the approximate solutions, some graphical illustrations in two- and three-dimensions are formally presented. Furthermore, several numerical tables are given to support the performance of the new analytical method in handling the time-fractional nonlinear water wave equation. (C) 2021 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 11
    Citation - Scopus: 11
    A Generalized Operational Matrix of Mixed Partial Derivative Terms With Applications To Multi-Order Fractional Partial Differential Equations
    (Elsevier, 2022) Jarad, Fahd; Mirza, Muhammad Umar; Nawaz, Asma; Riaz, Muhammad Bilal; Talib, Imran
    In this paper, a computational approach based on the operational matrices in conjunction with orthogonal shifted Legendre polynomials (OSLPs) is designed to solve numerically the multi-order partial differential equations of fractional order consisting of mixed partial derivative terms. Our computational approach has ability to reduce the fractional problems into a system of Sylvester types matrix equations which can be solved by using MATLAB builtin function lyap (.). The solution is approximated as a basis vectors of OSLPs. The efficiency and the numerical stability is examined by taking various test examples. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
  • Article
    Citation - WoS: 17
    Citation - Scopus: 18
    New Study of Weakly Singular Kernel Fractional Fourth-Order Partial Integro-Differential Equations Based on the Optimum Q-Homotopic Analysis Method
    (Elsevier, 2017) Darzi, Rahmat; Agheli, Bahram; Baleanu, Dumitru
    In this study, the optimum q-homotopic analysis method is employed to solve fourth order partial integro-differential equations with high-order non-integer derivatives. Several specific and clear examples are also given to illustrate the simplicity and capacity of the proposed approach. All of the computations were performed using Mathematica. (C) 2017 Elsevier B.V. All rights reserved.