# Asymptotic behavior of Eigenvalues and Eigenfunctions of T.Regge Fractional Problem

• Karwan Hama Faraj Jwamer * Department of Mathematics, College of Science, University of Sulaimani
• Hozan Dlshad Hilmi Department of Mathematics, College of Science, University of Sulaimani
Keywords: Regge Problem;, Fractional Integral;, Fractional Boundary problem;, Eigenvalue T.Regge;, Eigenfunction T.Regge

### Abstract

The asymptotic behavior of eigenvalues and eigenfunctions of T.Regge fractional boundary value problem has been shown, and we state and prove some theorems for many results, also some necessary definitions and results. In this paper, we look into a group of fractional boundary value problem equations involving fractional derivative fractional orders  and  with two boundary value conditions. We will which are important to state and prove those theorems; our primary findings are illustrated using examples.

### References

[1] K. B. Oldham and Jerome Spanier, The Fractional Calculus Theory and Applications of Differentiation and Integration to Arbitrary Order. New York: Academic press ,INC, 1974.
[2] J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of fractional calculus,” Commun. Nonlinear Sci. Numer. Simul., vol. 16, no. 3, pp. 1140–1153, 2011, doi: 10.1016/j.cnsns.2010.05.027.
[3] D. A. Zhuraev, “Cauchy Problem for Matrix Factorizations of the Helmholtz Equation,” Ukr. Math. J., vol. 69, no. 10, pp. 1583–1592, 2017, doi: 10.1007/s11253-018-1456-5.
[4] I. Podlubny, Fractional Differential Equations. San Diego: Elsevier, 1999.
[5] A. Carpinter and F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics. Springer-Verlag Wien GmbH, 1997.
[6] D. A. Juraev, “THE CAUCHY PROBLEM FOR MATRIX FACTORIZATIONS OF,” vol. 1, no. 3, pp. 312–319, 2018.
[7] M. A. Naimark, Linear Differential Operators, vol. 195, no. 4836. New York: Frederick Ungar, 1962.
[8] C. Milici, G. Draganescu, and J.Tenreiro Machado, Introduction to Fractional Differential Equations, vol. 25. Switzerland: Springer, 2019.
[9] K. S. Miller and B. Ross, “An introduction to the fractional calculus and fractional differential equations,” John-Wily and Sons. Wiley-Inter Science, New York, p. 9144, 1993.
[10] S. S. Ahmed, “On system of linear volterra integro-fractional differential equations,” no. July, 2009.
[11] Erwin Kreyszig, Introductory Functional Analysis with Applications, vol. 46, no. 1. John Wiley and Sons, 1989.
[12] K. Diethelm, The Analysis of Fractional Differential Equations. Springer, 2004.
[13] H. Hilmi and K. H. F. Jwamer, “Existence and Uniqueness Solution of Fractional Order Regge Problem,” vol. 30, no. 2, pp. 80–96, 2022.
[14] M. Klimek and O. P. Agrawal, “Fractional Sturm-Liouville problem,” Comput. Math. with Appl., vol. 66, no. 5, pp. 795–812, 2013, doi: 10.1016/j.camwa.2012.12.011.
Published
2022-09-24
How to Cite
Faraj Jwamer, K., & Hilmi, H. (2022). Asymptotic behavior of Eigenvalues and Eigenfunctions of T.Regge Fractional Problem. Journal of Al-Qadisiyah for Computer Science and Mathematics, 14(3), Math Page 89-100. https://doi.org/10.29304/jqcm.2022.14.3.1031
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Section
Math Articles