Fractional Derivatives as Inverses
Canadian journal of mathematics, Tome 41 (1989) no. 1, pp. 178-192

Voir la notice de l'article provenant de la source Cambridge University Press

We write formally (C, p) indicating that the integral is summable (C, p), i.e., if this limit exists. We note here that all integrals over a finite range are taken in the Lebesgue sense, and all inversions of such iterated integrals are justifiable by Fubini's Theorem.
Isaacs, Godfrey L. Fractional Derivatives as Inverses. Canadian journal of mathematics, Tome 41 (1989) no. 1, pp. 178-192. doi: 10.4153/CJM-1989-009-0
@article{10_4153_CJM_1989_009_0,
     author = {Isaacs, Godfrey L.},
     title = {Fractional {Derivatives} as {Inverses}},
     journal = {Canadian journal of mathematics},
     pages = {178--192},
     year = {1989},
     volume = {41},
     number = {1},
     doi = {10.4153/CJM-1989-009-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1989-009-0/}
}
TY  - JOUR
AU  - Isaacs, Godfrey L.
TI  - Fractional Derivatives as Inverses
JO  - Canadian journal of mathematics
PY  - 1989
SP  - 178
EP  - 192
VL  - 41
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1989-009-0/
DO  - 10.4153/CJM-1989-009-0
ID  - 10_4153_CJM_1989_009_0
ER  - 
%0 Journal Article
%A Isaacs, Godfrey L.
%T Fractional Derivatives as Inverses
%J Canadian journal of mathematics
%D 1989
%P 178-192
%V 41
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1989-009-0/
%R 10.4153/CJM-1989-009-0
%F 10_4153_CJM_1989_009_0

[1] 1. Andersen, A.F., Summation af ikke hel Orden, Mat. Tidsskrift, B (1946), 33–52. Google Scholar

[2] 2. Borwein, D., A summability factor theorem, J. London Math. Soc. 25 (1950), 302–315. Google Scholar

[3] 3. Bosanquet, L.S., On Liouville's extension of Abel's integral equation, Mathematika 16 (1969), 59–65. Google Scholar

[4] 4. Cossar, J., A theorem on Cesàro summability, J. London Math. Soc. 16 (1941), 56–68. Google Scholar

[5] 5. Isaacs, G.L., The iteration formula for inverted fractional integrals, Proc. London Math. Soc. (3) (1961), 213–238. Google Scholar

[6] 6. Isaacs, G.L., An iteration formula for fractional differences, Proc. London Math. Soc. (3. 13 (1963), 430–460. Google Scholar

[7] 7. Isaacs, G.L., Exponential laws for fractional differences, Math. Comp. 35 (1980), 933–936. Google Scholar

[8] 8. Whittaker, E.T. and Watson, G. N., A course of modern analysis (Cambridge University Press, London, 1940). Google Scholar

Cité par Sources :