WoS İndeksli Yayınlar Koleksiyonu

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

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Author: search.filters.author.Gomez-Aguilar, J. F.Subject: search.filters.subject.Fractional Calculus

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Now showing 1 - 4 of 4
  • Article
    Citation - WoS: 9
    Citation - Scopus: 11
    Correcting Dimensional Mismatch in Fractional Models With Power, Exponential and Proportional Kernel: Application To Electrical Systems
    (Elsevier, 2022) Correa-Escudero, I. L.; Gomez-Aguilar, J. F.; Lopez-Lopez, M. G.; Alvarado-Martinez, V. M.; Baleanu, D.
    Fractional calculus is a powerful tool for describing diffusion phenomena, anomalous behaviors, and in general, systems with highly complex dynamics. However, the application of fractional operators for modeling purposes, produces a dimensional problem. In this paper, the fractional models of the RC, RL, RLC electrical circuits, a supercapacitor, a bank of supercapacitors, a LiFePO4 battery and a direct current motor are presented. A correction parameter is included in their formulation in order to preserve dimensionality in the physical equations. The optimal value of this parameter was determined via particle swarm optimization algorithm using numerical simulations and experimental data. Thus, a direct and effective approach for the construction of dimensionally corrected fractional models with power, exponential-decay and constant proportional Caputo hybrid derivative is presented. To show the effectiveness of the procedure, the time-response of the models is compared with experimental data and the modeling error is computed. The numerical solutions of the models were obtained using a numerical method based on the Adams methods.
  • Article
    Citation - WoS: 26
    Citation - Scopus: 32
    On a More General Fractional Integration by Parts Formulae and Applications
    (Elsevier, 2019) Gomez-Aguilar, J. F.; Jarad, Fahd; Abdeljawad, Thabet; Atangana, Abdon
    The integration by part comes from the product rule of classical differentiation and integration. The concept was adapted in fractional differential and integration and has several applications in control theory. However, the formulation in fractional calculus is the classical integral of a fractional derivative of a product of a fractional derivative of a given function f and a function g. We argue that, this formulation could be done using only fractional operators: thus, we develop fractional integration by parts for fractional integrals, Riemann-Liouville, Liouville-Caputo, Caputo-Fabrizio and Atangana-Baleanu fractional derivatives. We allow the left and right fractional integrals of order alpha > 0 to act on the integrated terms instead of the usual integral and then make use of the fractional type Leibniz rules to formulate the integration by parts by means of new generalized type fractional operators with binomial coefficients defined for analytic functions. In the case alpha = 1, our formulae of fractional integration by parts results in previously obtained integration by parts in fractional calculus. The two disciplines or branches of mathematics are built differently, while classical differentiation is built with the concept of rate of change of a given function, a fractional differential operator is a convolution. (C) 2019 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 87
    Citation - Scopus: 95
    On Exact Solutions for Time-Fractional Korteweg-De Vries and Korteweg-De Vries-burger's Equations Using Homotopy Analysis Transform Method
    (Elsevier, 2020) AL-Shareef, Eman H. F.; Alomari, A. K.; Baleanu, Dumitru; Gomez-Aguilar, J. F.; Saad, K. M.
    In this paper we consider the homotopy analysis transform method (HATM) to solve the time fractional order Korteweg-de Vries (KdV) and Korteweg-de Vries-Burger's (KdVB) equations. The HATM is a combination of the Laplace decomposition method (LDM) and the homotopy analysis method (HAM). The fractional derivatives are defined in the Caputo sense. This method gives the solution in the form of a rapidly convergent series with h-curves are used to determine the intervals of convergent. Averaged residual errors are used to find the optimal values of h. It is found that the optimal h accelerates the convergence of the HATM, with the rate of convergence depending on the parameters in the KdV and KdVB equations. The HATM solutions are compared with exact solutions and excellent agreement is found.
  • Article
    Citation - WoS: 15
    Citation - Scopus: 17
    Fractional Dynamics of an Erbium-Doped Fiber Laser Model
    (Springer, 2019) Saad, K. M.; Baleanu, D.; Gomez-Aguilar, J. F.
    In this paper we investigate the model of the time-fractional dynamics of an erbium-doped fiber laser model (TFDEFL) with Liouville-Caputo (LC), Caputo-Fabrizio-Caputo (CFC) and Atangana-Baleanu-Caputo (ABC) time-fractional derivatives. We employ the homotopy analysis transform method (HATM) to calculate approximate solutions for the TFDEFL model. This method gives the solution in the form of a rapidly convergent series that can ensure the convergence in solving the resultant series. We study the convergence analysis of HATM by computing the interval of convergence through the h-curves, the residual error function and the average residual error, respectively. We also show the effectiveness and accuracy of this method by comparing the approximate solutions based upon the LC, CFC and ABC time-fractional derivatives.