Fractional dynamics of an erbium-doped fiber laser model
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Date
2019
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Springer
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Abstract
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.
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Fractional Calculus, Erbium-Doped Fiber Laser Model, Fractional Derivatives, Homotopy Analysis Transform Method, Analytical Solutions
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Citation
Gomez-Aguilar, J. F.; Saad, K. M.; Baleanu, D., "Fractional dynamics of an erbium-doped fiber laser model", Optical and Quantum Electronics, Vol. 51, No.9, (2019).
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Source
Optical and Quantum Electronics
Volume
51
Issue
9