# On Generalization of Sturm-Liouville Theory for Fractional Bessel Operator

Document Type : research paper

Author

Assistant Professor, Department of Pure Mathematics (Asymptotic Analysis)‎, ‎Faculty of ‎Mathematical Sciences‎, ‎University of Kashan‎, ‎Kashan 87317-53153‎, ‎Iran

Abstract

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal.

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal.

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal.

In this paper, we give the spectral theory for eigenvalues and eigenfunctions of a boundary value problem consisting of the linear fractional Bessel operator. Moreover, we show that this operator is self-adjoint, the eigenvalues of the problem are real, and the corresponding eigenfunctions are orthogonal.

Keywords

Article Title [فارسی]

### تعمیم نظریة استورم-لیوویل برای عملگر بسلِ کسری

Author [فارسی]

• سیدسیف‌اله موسی‌زاده
عضو هیئت علمی دانشکده علوم ریاضی دانشگاه کاشان
Abstract [فارسی]

در این مقاله، ‏نظریۀ طیفی را برای مقادیر ویژه و توابع ویژۀ یک مسألۀ مقدار مرزی شامل عملگر خطیِ بسلِ کسری ارائه می‌کنیم. بعلاوه ما نشان می‌دهیم که این عملگر، خودالحاقی است‏، مقادیر ویژۀ مسألۀ مقدار مرزی حقیقی هستند و توابع ویژۀ متناظرشان متعامدند.

Keywords [فارسی]

• مسألۀ مقدار مرزی
• مقادیر ویژه
• توابع ویژه
• نظریۀ طیفی

#### References

]1[ موسی‌زاده، سیدسیف‌اله، ریشه‌ها، مبانی و سیر تکاملی نظریۀ استورم-لیوویل، فرهنگ و اندیشۀ ریاضی، سال 36، شمارۀ 6، صص 67 تا 87، 1396.

[2] R. Kh. Amirov, V. A. Yurko. On differential operators with singularity and discontinuity conditions inside an interval. Ukrainian Mathematical Journal 53: 1751-1770(2001)

[3] W. N. Everitt, H. Kalf. The Bessel differential equation and the Hankel transform. Journal of Computational and Applied Mathematics 208: 3-19(2007)