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Fractional-order general Lagrange scaling functions and their applications

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Abstract

In this study, a general formulation for the fractional-order general Lagrange scaling functions (FGLSFs) is introduced. These functions are employed for solving a class of fractional differential equations and a particular class of fractional delay differential equations. For this approach, we derive FGLSFs fractional integration and delay operational matrices. These operational matrices and collocation method are utilized to reduce each of the problems to a system of algebraic equation, which can be solve employing Newton’s iterative method. We indicate convergence of this method. Finally, some illustrative examples in order to observe the validity, effectiveness and accuracy of the present technique are included. Also, by applying this method, we solve the mathematical model of the noise effect on the laser device.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran

    Sedigheh Sabermahani & Yadollah Ordokhani

  2. Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

    Sohrab Ali Yousefi

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  1. Sedigheh Sabermahani
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  2. Yadollah Ordokhani
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  3. Sohrab Ali Yousefi
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Correspondence to Yadollah Ordokhani.

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Communicated by Jan Hesthaven.

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Sabermahani, S., Ordokhani, Y. & Yousefi, S.A. Fractional-order general Lagrange scaling functions and their applications. Bit Numer Math 60, 101–128 (2020). https://doi.org/10.1007/s10543-019-00769-0

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