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Afarideh, Alireza, Dastmalchi Saei, Farhad, Nemati Saray, Behzad. (1402). Eigenvalue problem with fractional differential operator: Chebyshev cardinal spectral method. فیزیولوژی و بیوتکنولوژی آبزیان, 11(2), 343-355. doi: 10.22124/jmm.2023.24239.2169
Alireza Afarideh; Farhad Dastmalchi Saei; Behzad Nemati Saray. "Eigenvalue problem with fractional differential operator: Chebyshev cardinal spectral method". فیزیولوژی و بیوتکنولوژی آبزیان, 11, 2, 1402, 343-355. doi: 10.22124/jmm.2023.24239.2169
Afarideh, Alireza, Dastmalchi Saei, Farhad, Nemati Saray, Behzad. (1402). 'Eigenvalue problem with fractional differential operator: Chebyshev cardinal spectral method', فیزیولوژی و بیوتکنولوژی آبزیان, 11(2), pp. 343-355. doi: 10.22124/jmm.2023.24239.2169
Afarideh, Alireza, Dastmalchi Saei, Farhad, Nemati Saray, Behzad. Eigenvalue problem with fractional differential operator: Chebyshev cardinal spectral method. فیزیولوژی و بیوتکنولوژی آبزیان, 1402; 11(2): 343-355. doi: 10.22124/jmm.2023.24239.2169

Eigenvalue problem with fractional differential operator: Chebyshev cardinal spectral method

Journal of Mathematical Modeling
مقاله 8، دوره 11، شماره 2، مهر 2023، صفحه 343-355    اصل مقاله (232.64 K)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2023.24239.2169
نویسندگان
Alireza Afarideh1؛ Farhad Dastmalchi Saei* 1؛ Behzad Nemati Saray2
1Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran
2Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
چکیده
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.
کلیدواژه‌ها
collocation method؛ fractional Sturm-Liouville eigenvalue problem؛ Chebyshev cardinal functions
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تعداد مشاهده مقاله: 146
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