Eigenvalue problem with fractional differential operator: Chebyshev cardinal spectral method
Publish place: Journal of Mathematical Modeling، Vol: 11، Issue: 2
Publish Year: 1402
نوع سند: مقاله ژورنالی
زبان: English
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شناسه ملی سند علمی:
JR_JMMO-11-2_008
تاریخ نمایه سازی: 19 خرداد 1403
Abstract:
In this paper, we intend to introduce the Sturm-Liouville fractional problem and solve it using the collocation method based on Chebyshev cardinal polynomials. To this end, we first provide an introduction to the Sturm-Liouville fractional equation. Then the Chebyshev cardinal functions are introduced along with some of their properties and the operational matrices of the derivative, fractional integral, and Caputo fractional derivative are obtained for it. Here, for the first time, we solve the equation using the operational matrix of the fractional derivative without converting it to the corresponding integral equation. In addition to efficiency and accuracy, the proposed method is simple and applicable. The convergence of the method is investigated, and an example is presented to show its accuracy and efficiency.
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Authors
Alireza Afarideh
Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
Farhad Dastmalchi Saei
Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
Behzad Nemati Saray
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan ۴۵۱۳۷-۶۶۷۳۱, Iran