Publication Cover
Applicable Analysis
An International Journal
Volume 76, 2000 - Issue 3-4
85
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

Stability results for fractional differentiation

&
Pages 249-260 | Received 01 Dec 1999, Published online: 10 May 2007

References

  • Hào , Dinh Nho . 1994 . A modification method for ill posed problem . Number. Math , 68 : 469 – 506 .
  • Hào , Dinh Nho , Reinhardt , H.J. and Seiffarth , F. 1994 . Stable numerical fracetional differentiation by mollification . Numer. Funct. Anal. and Optimiz , 15 : 635 – 659 .
  • Gorenflo , R. 1986 . Approximation of discrete probabilty distributions in spherical stereology . International Series of Numerical Mathematics , 77 : 103 – 115 .
  • Gorenflo , R. 1987 . “ Compution of rough solutions of Abel integral euations ” . In Inverse and Ill Posed Problems , Edited by: Engl , H.W. and Groestch , C.W. 195 – 210 . Boston : Academic Press .
  • Gorenflo , R. , Medvedeva , T. and Rubin , B. 1997 . Locally controllable regularization of Abel integral equations via operator complementation . J. Inverse Ill Posed Problems , 5 : 427 – 436 .
  • Gorenflo , R. and Vessella , S. 1991 . Abel Integral Equations .
  • Gorenflo , R. and Rubin , B. 1994 . Locally controllable regularization of fractional derivatives . Inverse problems , 10 : 881 – 893 .
  • Krein , M.G. 1943 . On the representation of functions by Fouries Stieltjes integrals . Ucen. Zap. Kuibysev. Ped. Inst , 7 : 123 – 148 . Russian
  • Lizorkin , P.I. 1968 . Estimates for itrigonometric integrals and the Bernstein inequality for fractional derivatives . English Transl.: AMS Transl , 77 ( 2 ) : 45 – 62 . Izv. AN SSSR, Ser. Math. 29(1965), 109-126
  • Lizorkin , P.I. 1963 . Generalized Liouville differentiation and functional spaces Lr p(En) . Embedding theorems. Math.Sb , 60 : 325 – 353 . Russian
  • Nikol'skii , S.M. 1975 . Approximation of Functions of Several Variables and Imbedding Theorems .
  • Rubin , B. 1996 . Fractional Integrals and Potentials .
  • Samko , S. , Kilbas , A.A. and Marichev , O.I. 1993 . “ Fractional Integrals and derivatives ” . In Theory and Applications , London : Gordon and Breach .
  • Tuan , Vu Kim and Gorenflo , R. 1994 . The Grünwald Letnilov difference operator and regularization of the Weyl fractional differentiation . Z. Anal. Anwendungen , 13 : 537 – 545 .
  • Tuan , Vu Kim and Gorenflo , R. 1994 . On the regularization of fractional differentiation of arbitrary positive order . Number. Funct. Anal. Optim , 15 : 695 – 711 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.