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Massah Maralani, Elnaz, Dastmalchi Saei, Farhad, Jodayree Akbarfam, Ali Asghar, Ghanbari, Kazem. (1400). Eigenvalues of fractional Sturm-Liouville problems by successive method. سامانه مدیریت نشریات علمی, 9(4), 1163-1175. doi: 10.22034/cmde.2020.37867.1671
Elnaz Massah Maralani; Farhad Dastmalchi Saei; Ali Asghar Jodayree Akbarfam; Kazem Ghanbari. "Eigenvalues of fractional Sturm-Liouville problems by successive method". سامانه مدیریت نشریات علمی, 9, 4, 1400, 1163-1175. doi: 10.22034/cmde.2020.37867.1671
Massah Maralani, Elnaz, Dastmalchi Saei, Farhad, Jodayree Akbarfam, Ali Asghar, Ghanbari, Kazem. (1400). 'Eigenvalues of fractional Sturm-Liouville problems by successive method', سامانه مدیریت نشریات علمی, 9(4), pp. 1163-1175. doi: 10.22034/cmde.2020.37867.1671
Massah Maralani, Elnaz, Dastmalchi Saei, Farhad, Jodayree Akbarfam, Ali Asghar, Ghanbari, Kazem. Eigenvalues of fractional Sturm-Liouville problems by successive method. سامانه مدیریت نشریات علمی, 1400; 9(4): 1163-1175. doi: 10.22034/cmde.2020.37867.1671

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
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