On the number of real eigenvalues of a certain boundary-value problem for a second-order equation with fractional derivative

Journal of Mathematical Sciences

Volumn 151, Issue 1, 2008, Pages 2726-2740

  Popov, A Yu ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 42449160660     PISSN: 10723374     EISSN: 15738795     Source Type: Journal    
DOI: 10.1007/s10948-008-0169-7     Document Type: Article

References (11)

1. N. K. Bari, Trigonometric Series [in Russian], Fizmatgiz, Moscow (1961).
2. H. Bateman and A. Erdelyi, Higher Transcendental Functions [Russian translation], Vol. 3, Nauka, Moscow (1967).
3. M. M. Dzhrbashyan, Integral Transforms and Representations of Functions in a Complex Domain [in Russian], Nauka, Moscow (1966).
4. M. M. Dzhrbashyan, "Boundary-value problem for a fractional-order differential operators of the Sturm-Liouville type," Izv. Akad. Nauk Arm. SSR, Ser. Mat., 5, No. 2, 71-96 (1970).
5. L. P. Kuptsov, "Gamma-function," in: Mathematical Encyclopaedia [in Russian], Vol. 1, Moscow (1977), pp. 866-869
6. A. M. Nakhushev, "Sturm-Liouville problem for a second-order differential equation with fractional derivatives in lower-order terms," Dokl. Akad. Nauk SSSR, 234, No. 2, 308-311 (1977).
7. A. M. Nakhushev, Fractional Calculus and Its Applications [in Russian], Fizmatlit, Moscow (2003).
8. ρ (z,μ)," Anal. Math., 23, 283-296 (1997).
9. A. V. Pskhu, "On real zeros of a Mittag-Leffler-type function," Mat. Zametki, 77, No. 4, 592-599 (2005).
10. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Fractional-Order Integrals and Series and Some of Their Applications [in Russian], Minsk (1987).
11. A. M. Sedletskii, "Nonasymptotic properties of roots of a Mittag-Leffler-type function," Mat. Zametki, 75, No. 3, 405-420 (2004).