Eigenvalues of fractional Sturm-Liouville problems by successive method

Massah Maralani, Elnaz; Dastmalchi Saei, Farhad; Jodayree Akbarfam, Ali Asghar; Ghanbari, Kazem

doi:10.22034/cmde.2020.37867.1671

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	Eigenvalues of fractional Sturm-Liouville problems by successive method
Computational Methods for Differential Equations
مقاله 16، دوره 9، شماره 4، دی 2021، صفحه 1163-1175 اصل مقاله (291.8 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.37867.1671
نویسندگان
Elnaz Massah Maralani¹؛ Farhad Dastmalchi Saei^* ¹؛ Ali Asghar Jodayree Akbarfam²؛ Kazem Ghanbari³
¹Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
²Department of Applied Mathematics, Mathematical Science Faculty, University of Tabriz, Tabriz, Iran.
³Department of Mathematics, Sahand University of Technology, Tabriz, Iran.
چکیده
In this paper, we consider a fractional Sturm-Liouville equation of the form, − cDα 0+ ◦ Dα 0+ y(t) + q(t)y(t) = λy(t), 0 < α < 1, t ∈ [0, 1], with Dirichlet boundary conditions I 1−α 0+ y(t)\|t=0 = 0, and I 1−α 0+ y(t)\|t=1 = 0, where, the sign ◦ is composition of two operators and q ∈ L2 (0, 1), is a real valued potential function. We use a recursive method based on Picard’s successive method to find the solution of this problem. We prove the method is convergent and show that the eigenvalues are obtained from the zeros of the Mittag-Leffler function and its derivatives.
کلیدواژه‌ها
Fractional Sturm-Liouville؛ Fractional calculus؛ Sucssesive methods؛ Eigenvalues

مراجع
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Eigenvalues of fractional Sturm-Liouville problems by successive method