Debbi, Latifa2015-10-012015-10-012007https://dspace.univ-boumerdes.dz/handle/123456789/2274A fractional differential operator of order α ∈ R+ is introduced and some of its properties are studied. This operator is a generalization of the operators of Riesz-Feller, of Riemann-Liouville, of the fractional power of the Laplacian and of a class of the Jacob pseudodifferential operators. Mathematics Subject Classification: 26A33, 35S05, 60G52enGeneral SelfadjointHigh Order FractionalArticle