A note on fractional spaces generated by the positive operator with periodic conditions and applications

Boundary Value Problems

Volumn 2015, Issue 1, 2015, Pages

  Ashyralyev, Allaberen ^a,b   Tetikoglu, Fatih Sabahattin ^a  

^a FATIH UNIVERSITY   (Turkey)

^b ITTU   (Turkmenistan)

Author keywords

boundary value problems; fractional spaces; Green function; positive operator

Indexed keywords

EID: 84922779788     PISSN: 16872762     EISSN: 16872770     Source Type: Journal    
DOI: 10.1186/s13661-015-0293-9     Document Type: Article

References (25)

1. Krein, SG: Linear Differential Equations in a Banach Space. Translations of Mathematical Monographs. Am. Math. Soc., Providence (1968)
2. Fattorini, HO: Second Order Linear Differential Equations in Banach Spaces. Elsevier, Amsterdam (1985)
3. Sobolevskii, PE: A new method of summation of Fourier series converging in C-norm. Semigroup Forum 71, 289-300 (2005)
4. Ashyralyev, A, Sobolevskii, PE (eds.): Well-Posedness of Parabolic Difference Equations. Operator Theory: Advances and Applications, vol. 69. Birkhäuser, Basel (1994)
5. Ashyralyev, A, Sobolevskii, PE (eds.): New Difference Schemes for Partial Differential Equations. Operator Theory: Advances and Applications, vol. 148. Birkhäuser, Basel (2004)
6. Ashyralyev, A, Yaz, N: On structure of fractional spaces generated by positivity operators with the nonlocal boundary conditions. In: Differential & Difference Equations and Applications, pp. 91-102. Hindawi Publishing Corporation, New York (2006)
7. Alibekov, KA, Sobolevskii, PE: Stability of difference schemes for parabolic equations. Dokl. Akad. Nauk SSSR 232(4), 737-740 (1977)
8. Ashyralyev, A: Method of positive operators of investigations of the high order of accuracy difference schemes for parabolic and elliptic equations. Ph.D. thesis, Inst. of Math. of Acad. Sci., Kiev (1992)
9. Ashyralyev, A, Nalbant, N, Sözen, Y: Structure of fractional spaces generated by second order difference operators. J. Franklin Inst. Eng. Appl. Math. 351(2), 713-731 (2014). doi:10.1016/j.jfranklin.2013.07.009
10. Ashyralyev, A, Sobolevskii, PE: The linear operator interpolation theory and the stability of difference-schemes. Dokl. Akad. Nauk SSSR 275(6), 1289-1291 (1984) (in Russian)
11. Ashyralyev, A, Tetikoglu, FS: The structure of fractional spaces generated by the positive operator with periodic conditions. In: Ashyralyev, A, Lukashov, A (eds.) First International Conference on Analysis and Applied Mathematics: ICAAM 2012. AIP Conference Proceedings, vol. 1470, pp. 57-60 (2012)
12. Agmon, S (ed.): Lectures on Elliptic Boundary-Value Problems. Van Nostrand, Princeton (1996)
13. Semenova, GE: Positivity of elliptic difference operators and its applications. In: Ashyralyev, A, Lukashov, A (eds.) First International Conference on Analysis and Applied Mathematics: ICAAM 2012. AIP Conference Proceedings, vol. 1470, pp. 232-235 (2012)
14. Solomyak, MZ: Analytic semigroups generated by elliptic operator in spaces (Formula presented.). Dokl. Akad. Nauk SSSR 127(1), 37-39 (1959)
15. Solomyak, MZ: Estimation of norm of the resolvent of elliptic operator in spaces (Formula presented.). Usp. Mat. Nauk 15(6), 141-148 (1960)
16. Danelich, SI: Positive difference operators in Rh1$R_{h1}$. Voronezh. Gosud Univ. 1987, Deposited VINITI 3.18, no. 1936-B87, 13 (1989)
17. Ashyralyev, A: Fractional spaces generated by the positive differential and difference operators in a Banach space. In: ISMME, vol. 83, pp. 10-19. Springer, Berlin (2006)
18. Ashyralyev, A, Yakubov, A: The structures of fractional spaces generating by the transport operator. In: Modeling the Processes in Exploration of Gas Deposits and Applied Problems of Theoretical Gas Hydrodynamics, pp. 162-172 (1998)
19. Bazarov, MA: On the structure of fractional spaces. In: Proceedings of the XXVII All-Union Scientific Student Conference ‘The Student and Scientific-Technological Progress’ (Novosibirsk, 1989), pp. 3-7. Novosibirsk. Gos. Univ., Novosibirsk (1989)
20. Simirnitskii, YA, Sobolevskii, PE: Positivity of multidimensional difference operators in the C-norm. Usp. Mat. Nauk 36(4), 202-203 (1981)
21. Simirnitskii, YA, Sobolevskii, PE: Pointwise estimates of the Green function of the resolvent of a difference elliptic operator. Čisl. Metody Meh. Sploš. Sredy 13(4), 129-142 (1982)
22. Ashyralyev, A, Akturk, S, Sozen, Y: The structure of fractional spaces generated by a two-dimensional elliptic differential operator and its applications. Bound. Value Probl. 2014, Article ID 3 (2014). doi:10.1186/1687-2770-2014-3
23. Smirnitskii, YA, Sobolevskii, A (eds.): Positivity of difference operators. In: Spline Methods, Novosibirsk (1981) (in Russian)
24. Ashyralyev, A, Agirseven, D: Stability of parabolic equations with unbounded operators acting on delay terms. Electron. J. Differ. Equ. 2014, 160 (2014)
25. Ashyralyev, A: On well-posedness of the nonlocal boundary value problems for elliptic equations. Numer. Funct. Anal. Optim. 24, 1-15 (2003)