Geodesic
Generalized Fractional Evolution Equation
Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 375-398.

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

In this paper we study the generalized Riemann-Liouville (resp. Caputo) time fractional evolution equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function. The fundamental solution corresponding to the Riemann-Liouville time fractional evolution equation does not admit a probabilistic representation while for the Caputo time fractional evolution equation it is related to the inverse stable subordinators.
Keywords: Generalized Functions, Convolution Product, Generalized Gross Laplacian, Riemann-Liouville Derivative, Caputo Derivative, 46F25, 26A33, 46G20 
@article{FCAA_2007_10_4_a2,
     author = {Da Silva, J. L. and Erraoui, M. and Ouerdiane, H.},
     title = {Generalized {Fractional} {Evolution} {Equation}},
     journal = {Fractional calculus and applied analysis},
     pages = {375--398},
     publisher = {mathdoc},
     volume = {10},
     number = {4},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a2/}
}
TY  - JOUR
AU  - Da Silva, J. L.
AU  - Erraoui, M.
AU  - Ouerdiane, H.
TI  - Generalized Fractional Evolution Equation
JO  - Fractional calculus and applied analysis
PY  - 2007
SP  - 375
EP  - 398
VL  - 10
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a2/
LA  - en
ID  - FCAA_2007_10_4_a2
ER  - 
%0 Journal Article
%A Da Silva, J. L.
%A Erraoui, M.
%A Ouerdiane, H.
%T Generalized Fractional Evolution Equation
%J Fractional calculus and applied analysis
%D 2007
%P 375-398
%V 10
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a2/
%G en
%F FCAA_2007_10_4_a2
Da Silva, J. L.; Erraoui, M.; Ouerdiane, H. Generalized Fractional Evolution Equation. Fractional calculus and applied analysis, Tome 10 (2007) no. 4, pp. 375-398. http://geodesic.mathdoc.fr/item/FCAA_2007_10_4_a2/