An operator theoretical approach to a class of fractional order differential equations

Applied Mathematics Letters

Volumn 24, Issue 2, 2011, Pages 184-190

  Lizama, Carlos ^a  

^a UNIVERSIDAD DE SANTIAGO DE CHILE   (Chile)

Author keywords

Fractional order derivative; Linear unbounded operator; Regularized resolvent family

Indexed keywords

CLOSED OPERATOR; FRACTIONAL ORDER; FRACTIONAL ORDER DERIVATIVES; GENERAL METHOD; REGULARIZED RESOLVENT FAMILIES; THEORETICAL APPROACH; UNBOUNDED OPERATORS;

BANACH SPACES; DIFFERENTIAL EQUATIONS; TOPOLOGY;

MATHEMATICAL OPERATORS;

EID: 78049480821     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2010.08.042     Document Type: Article

References (23)

1. D. Araya, and C. Lizama Almost automorphic mild solutions to fractional differential equations Nonlinear Anal. TMA 69 2008 3692 3705
2. E. Bazhlekova, Fractional evolution equations in Banach spaces, Ph.D. Thesis, Eindhoven University of Technology, 2001.
3. R. Hilfer Applications of Fractional Calculus in Physics 2000 World Scientific Publ. Co. Singapore
4. A.A. Kilbas, H.M. Srivastava, and J.J. Trujillo Theory and Applications of Fractional Differential Equations 2006 Elsevier Amsterdam
5. N. Heymans, and I. Podlubny Physical interpretation of initial conditions for fractional differential equations with RiemannLiouville fractional derivatives Rheol. Acta 45 5 2006 765 771
6. I. Podlubny Fractional Differential Equations 1999 Academic Press San Diego
7. S.G. Samko, A.A. Kilbas, and O.I. Marichev Fractional Integrals and Derivatives: Theory and Applications 1993 Gordon and Breach New York Translation from the Russian edition, Nauka i Tekhnika, Minsk (1987)
8. R. Gorenflo, F. Mainardi, Fractional Calculus: Integral and Differential Equations of Fractional Order, in: CIMS Lecture Notes, 1997, http://arxiv.org/0805.3823.
9. B. Baeumer, M.M. Meerschaert, and E. Nane Brownian subordinators and fractional Cauchy problems Trans. Amer. Math. Soc. 361 7 2009 3915 3930
10. E. Nane Higher order PDE's and iterated processes Trans. Amer. Math. Soc. 360 5 2008 2681 2692
11. V. Keyantuo, C. Lizama, On a connection between powers of operators and fractional Cauchy problems (submitted for publication).
12. J. Prss Evolutionary Integral Equations and Applications Monographs Math. vol. 87 1993 Birkhuser Verlag
13. R. Gorenflo, and F. Mainardi On MittagLeffler-type functions in fractional evolution processes J. Comput. Appl. Math. 118 2000 283 299
14. R. Gorenflo, and F. Mainardi Fractional Calculus: Integral and Differential Equations of Fractional Order A. Carpinteri, F. Mainardi, Fractals and Fractional Calculus in Continuum Mechanics 1997 Springer-Verlag Vienna, New York 223 276
15. W. Arendt, C. Batty, M. Hieber, and F. Neubrander Vector-Valued Laplace Transforms and Cauchy Problems Monographs in Mathematics vol. 96 2001 Birkhuser Basel
16. C. Lizama Regularized solutions for abstract Volterra equations J. Math. Anal. Appl. 243 2000 278 292
17. M. Kostic (a, k ) -regularized C-resolvent families: regularity and local properties Abstr. Appl. Anal. 2009 2009 10.1155/2009/858242 Article ID 858242, 27 pages
18. C. Lizama On approximation and representation of k-regularized resolvent families Integral Equations Operator Theory 41 2 2001 223 229
19. C. Lizama, and H. Prado Rates of approximation and ergodic limits of regularized operator families J. Approx. Theory 122 1 2003 42 61
20. C. Lizama, and J. Snchez On perturbation of k-regularized resolvent families Taiwanese J. Math. 7 2 2003 217 227
21. C. Lizama, and H. Prado On duality and spectral properties of (a, k ) -regularized resolvents Proc. Roy. Soc. Edinburgh Sect. A 139 3 2009 505 517
22. S.Y. Shaw, and J.C. Chen Asymptotic behavior of (a, k ) -regularized families at zero Taiwanese J. Math. 10 2 2006 531 542
23. K.J. Engel, and R. Nagel One-Parameter Semigroups for Linear Evolution Equations Graduate Texts in Math. vol. 194 2000 Springer New York, Berlin, Heidelberg