CONFORMABLE EIGENVALUE PROBLEMS WITH TWO PARAMETERS

Year 2024, Volume: 7 Issue: To memory "Assoc. Prof. Dr. Zeynep AKDEMİRCİ ŞANLI", 10 - 22, 29.12.2024

Aslı Öner , Sertaç Göktaş , Büşra Barut

https://doi.org/10.33773/jum.1546765

Abstract

This study used conformable derivatives to define the eigenvalue problems with two parameters and examined various associated spectral properties. Firstly, the conformable eigenvalue problems with two parameters were reduced to the simpler one parameter problems. Additionally, we focused on the orthogonality properties of eigenfunctions. Secondly, investigating the reality of eigenvalues is important to understand the physical relevance and practical usability of the considered eigenvalue problem. Finally, we examined integral relations, which explain important connections and relationships between different aspects of the problem.

Keywords

Conformable Derivative, Sturm-Liouville Problems, Two Parameter Eigenvalue Problems

References

• T. Abdeljawad, On conformable fractional calculus, Journal of computational and Applied Mathematic, Vol.279, pp. 57-66 (2015).
• B. P. Allahverdiev, E. Bairamov, E. Ugurlu, Eigenparameter dependent Sturm–Liouville problems in boundary conditions with transmission conditions, Journal of Mathematical Analysis and Applications, Vol.401, No.1, pp. 388-396 (2013).
• B. P. Allahverdiev, H. Tuna, Y. Yalcinkaya, Conformable fractional Sturm‐Liouville equation, Mathematical Methods in the Applied Sciences, Vol.42, No.10, pp. 3508-3526 (2019).
• M. Al-Refai, T. Abdeljawad, Fundamental results of conformable Sturm‐Liouville eigenvalue problems, Complexity, Vol.2017, No.1, pp. 3720471 (2017).
• F. M. Arscott, Integral equations for ellipsoidal wave functions, The Quarterly Journal Of Mathematics, Vol.8, No.1, pp. 223--235 (1957).
• F. M. Arscott, A New Treatment of the ellipsoidal wave equation, Proceedings Of The London Mathematical Society, Vol.3, No.1, pp. 21--50 (1959).
• F. M. Arscott, Two-parameter eigenvalue problems in differential equations, Proceedings Of The London Mathematical Society, Vol.3, No.3, pp. 459-470 (1964).
• F. V. Atkinson, A. B. Mingarelli, Multiparameter eigenvalue problems, New York: Academic Press, Vol.1, (1972).
• E. Bairamov, Y. Aygar, G. B. Oznur, Scattering properties of eigenparameter-dependent impulsive Sturm–Liouville equations, Bulletin of the Malaysian Mathematical Sciences Society, Vol.43, pp. 2769-2781 (2020).
• O. Cabri, K. R. Mamedov, On the riesz basisness of root functions of a sturm–liouville operator with conjugate conditions, Lobachevskii Journal of Mathematics, Vol.41, pp. 1784-1790 (2020).
• S. Goktas, H. Koyunbakan, T. Gulsen, Inverse nodal problem for polynomial pencil of Sturm‐Liouville operator, Mathematical Methods in the Applied Sciences, Vol.41, No.17, pp. 7576-7582 (2018).