Geodesic
Partial differential equations/Mathematical physics
A theorem on the existence of symmetries of fractional PDEs
[Un théorème sur l'existence de symétries pour les équations aux derivées partielles fractionnaires]

Présenté par : Pierre-Louis Lions

Leo, Rosario Antonio1 ; Sicuro, Gabriele2 ; Tempesta, Piergiulio3, 4
1 Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Via per Arnesano, 73100 Lecce, Italy
2 Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Italy
3 Departamento de Fisica Teorica II, Métodos Matemáticos de la Física, Universidad Complutense de Madrid, Ciudad Universitaria, 28040, Madrid, Spain
4 Instituto de Ciencias Matemáticas, C/ Nicolás Cabrera, No 13-15, 28049 Madrid, Spain
Comptes Rendus. Mathématique, Tome 352 (2014) no. 3, pp. 219-222.

Voir la notice de l'article provenant de la source Numdam

We propose a theorem that extends the classical Lie approach to the case of fractional partial differential equations (fPDEs) of the Riemann–Liouville type in (1+1) dimensions.

Nous proposons un théorème qui generalise la méthode classique de Lie à l'étude d'équations aux derivées partielles fractionnaires de type Riemann–Liouville en (1+1) dimensions.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2013.11.007

Leo, Rosario Antonio 1 ; Sicuro, Gabriele 2 ; Tempesta, Piergiulio 3, 4

1 Dipartimento di Matematica e Fisica “Ennio De Giorgi”, Università del Salento, Via per Arnesano, 73100 Lecce, Italy
2 Dipartimento di Fisica “Enrico Fermi”, Università di Pisa, Italy
3 Departamento de Fisica Teorica II, Métodos Matemáticos de la Física, Universidad Complutense de Madrid, Ciudad Universitaria, 28040, Madrid, Spain
4 Instituto de Ciencias Matemáticas, C/ Nicolás Cabrera, No 13-15, 28049 Madrid, Spain 
@article{CRMATH_2014__352_3_219_0,
     author = {Leo, Rosario Antonio and Sicuro, Gabriele and Tempesta, Piergiulio},
     title = {A theorem on the existence of symmetries of fractional {PDEs}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {219--222},
     publisher = {Elsevier},
     volume = {352},
     number = {3},
     year = {2014},
     doi = {10.1016/j.crma.2013.11.007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2013.11.007/}
}
TY  - JOUR
AU  - Leo, Rosario Antonio
AU  - Sicuro, Gabriele
AU  - Tempesta, Piergiulio
TI  - A theorem on the existence of symmetries of fractional PDEs
JO  - Comptes Rendus. Mathématique
PY  - 2014
SP  - 219
EP  - 222
VL  - 352
IS  - 3
PB  - Elsevier
UR  - http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2013.11.007/
DO  - 10.1016/j.crma.2013.11.007
LA  - en
ID  - CRMATH_2014__352_3_219_0
ER  - 
%0 Journal Article
%A Leo, Rosario Antonio
%A Sicuro, Gabriele
%A Tempesta, Piergiulio
%T A theorem on the existence of symmetries of fractional PDEs
%J Comptes Rendus. Mathématique
%D 2014
%P 219-222
%V 352
%N 3
%I Elsevier
%U http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2013.11.007/
%R 10.1016/j.crma.2013.11.007
%G en
%F CRMATH_2014__352_3_219_0
Leo, Rosario Antonio; Sicuro, Gabriele; Tempesta, Piergiulio. A theorem on the existence of symmetries of fractional PDEs. Comptes Rendus. Mathématique, Tome 352 (2014) no. 3, pp. 219-222. doi : 10.1016/j.crma.2013.11.007. http://geodesic.mathdoc.fr/articles/10.1016/j.crma.2013.11.007/

[1] Buckwar, E.; Luchko, Y. Invariance of a partial differential equation of fractional order under the Lie group of scaling transformations, J. Math. Anal. Appl., Volume 227 (1998), pp. 81-97

[2] Gazizov, R.K.; Kasatkin, A.A.; Lukashchuk, S.Y.; Gazizov, R.K.; Kasatkin, A.A.; Lukashchuk, S.Y., Phys. Scr. T (Machado, J.A.T.; Luo, A.C.J.; Barbosa, R.S.; Silva, M.F.; Figueiredo, L.B., eds.) (Group-invariant solutions of fractional differential equations, Nonlinear Science and Complexity), Volume 136, Springer, 2009, pp. 51-58

[3] Gorenflo, R.; Luchko, Yu.; Mainardi, F. Wright functions as scale-invariant solutions of the diffusion-wave equation, J. Comput. Appl. Math., Volume 11 (2000), pp. 175-191

[4] Luchko, Yu.; Gorenflo, R. Scale-invariant solutions of a partial differential equation of fractional order, Fract. Calc. Appl. Anal., Volume 1 (1998), pp. 63-78

[5] Olver, P.J. Applications of Lie Groups to Differential Equations, Springer, 1986

[6] Osler, T.J. Leibniz rule for fractional derivatives generalized and an application to infinite series, SIAM J. Appl. Math., Volume 18 (1970) no. 3, pp. 658-674

[7] Samko, S.G.; Kilbas, A.A.; Marichev, O.I. Fractional Integrals and Derivatives. Theory and Applications, Gordon and Breach Science Publishers, 1993

Cité par Sources :