On a Riemann-Liouville fractional analog of the Laplace operator with positive energy

Integral Transforms and Special Functions

Volumn 23, Issue 4, 2012, Pages 277-295

  Dalla Riva, M ^a   Yakubovich, S ^a  

^a UNIVERSITY OF PORTO   (Portugal)

Author keywords

boundary value problems; fractional analog of Laplace operator; integration by parts; Riemann Liouville integrals and derivative

Indexed keywords

EID: 84859401607     PISSN: 10652469     EISSN: 14768291     Source Type: Journal    
DOI: 10.1080/10652469.2011.576832     Document Type: Article

References (10)

1. Bogdan, K. 1997. The boundary Harnack principle for the fractional Laplacian. Studia Math, 123(1): 43-80.
2. Caffarelli, L. A., Salsa, S. and Silvestre, L. 2008. Regularity estimates for the solution and the free boundary of the obstacle problem for the fractional Laplacian. Invent. Math, 171(2): 425-461.
3. Guan, Q. Y. 2006. Integration by parts formula for regional fractional Laplacian. Comm. Math. Phys, 266(2): 289-329.
4. Guan, Q. Y. and Ma, Z. M. 2005. Boundary problems for fractional Laplacians. Stochast. Dyn, 5(3): 385-424.
5. Krasnosel′skiui{dotless}, P. P., Zabreii{dotless}ko, M. A., Pustyl′nik, E. I. and Sobolevskiii{dotless}, P. E. 1976. Integral Operators in Spaces of Summable Functions, Leiden: Noordhoff International Publishing.
6. Lopushans′ka, G. P. 1999. Fundamental boundary value problems for an equation in fractional derivatives. Ukrainian Math. J, 51(1): 51-65.
7. Mikhlin, S. G. and Prössdorf, S. 1986. Singular integral operators volume 68 of Mathematische Lehrbücher und Monographien, II. Abteilung: Mathematische Monographien [Mathematical Textbooks and Monographs, Part II: Mathematical Monographs], Berlin: Akademie-Verlag.
8. Samko, S. G. 2002. Hypersingular Integrals and their Applications Volume 5 of Analytical Methods and Special Functions, London: Taylor & Francis.
9. Samko, S. G., Kilbas, A. A. and Marichev, O. I. 1993. Fractional Integrals and Derivatives, Yverdon: Gordon and Breach Science Publishers.
10. Yakubovich, S. 2010. Eigenfunctions and fundamental solutions of the fractional two-parameter laplacian. Int. J. Math. Math. Sci, (2010), 18 pages. Article ID 541934. Available athttp://www.hindawi.com/journals/ijmms/2010/541934/2010/541934/