Existence and uniqueness results for a fractional evolution equation in hilbert space

Fractional Calculus and Applied Analysis

Volumn 15, Issue 2, 2012, Pages 232-243

  Bazhlekova, Emilia ^a  

^a INSTITUTE OF MATHEMATICS AND INFORMATICS   (Bulgaria)

Author keywords

Accretive operator; Fractional evolution equation; Kernel of positive type; Maximal regularity; Subdiffusion equation

Indexed keywords

EID: 84869180066     PISSN: 13110454     EISSN: 13142444     Source Type: Journal    
DOI: 10.2478/s13540-012-0017-0     Document Type: Article

References (18)

1. B. Baeumer, S. Kurita, M.M. Meerschaert, Inhomogeneous fractional diffusion equations. Fract. Calc. Appl. Anal. 8, No 4 (2005), 371-386; at http://www.math.bas.bg/fcaa
2. E. Bajlekova, Fractional Evolution Equations in Banach Spaces. PhD Thesis, Eindhoven University of Technology (2001); at http://alexandria.tue.nl/ extra2/200113270.pdf
3. H. Brezis, Op'erateurs Maximaux Monotones et Semi-groupes de Contractions dans les Espaces de Hilbert. Math. Studies 5, North-Holland, Amsterdam (1973).
4. Ph. Cĺement, S.-O. Londen, On the sum of fractional derivatives and m-accretive operators. Partial Differential Equations /Models in Physics and Biology, Mathematical Research 64, Academie Verlag Berlin (1994), 91-100.
5. G. Dore, A. Venni, On the closedness of the sum of two closed operators. Math. Z. 196 (1987), 189-201.
6. P. Egberts, On the Sum of Accretive Operators. Ph.D. Thesis, TU Delft (1992).
7. N. Heymans, I. Podlubny, Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives. Rheologica Acta 45, No 5 (2006), 765-772.
8. R. Hilfer, Fractional diffusion based on Riemann-Liouville fractional derivative. J. Phys. Chem. B 104, No 16 (2000), 3914-3917.
9. T. Kato, Perturbation Theory for Linear Operators. Springer-Verlag Berlin, Heidelberg, New-York (1966).
10. T. Kato, Remarks on pseudo-resolvents and infinitesimal generators of semi-groups. Proc. Japan Acad. 35 (1959), 467-468.
11. A.A. Kilbas, H.M. Srivastava, J.J. Trujillo, Theory and Applications of Fractional Differential Equations. North-Holland Mathematics Studies, Elsevier (2006).
12. A.N. Kochubei, A Cauchy problem for evolution equations of fractional order. Diff. Equations 25 (1989), 967-974.
13. A.N. Kochubei, Distributed order calculus and equations of ultraslow diffusion. J. Math. Anal. Appl. 340, No 1 (2008), 252-281.
14. Y. Luchko, Initial-boundary-value problems for the one-dimensional time-fractional diffusion equation. Fract. Calc. Appl. Anal. 15, No 1 (2012), 141-160; DOI: 10.2478/s13540-012-0010-7; http://www.springerlink.com/content/ 1311-0454/15/1/
15. R. Metzler, J. Klafter, The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics. J. Phys. A. Math. Gen. 37 (2004), R161-R208.
16. J. Pruss, Evolutionary Integral Equations and Applications. Birkhauser, Basel, Boston, Berlin (1993).
17. Ya.E. Ryabov, Behavior of fractional diffusion at the origin. Physical Review E 68 (2003) 030102(R).
18. S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, New York (1993).