On time fractional derivatives in fractional Sobolev spaces and applications to fractional ordinary differential equations
The author of this article formulates two kinds of time fractional derivatives of Caputo type with order α in fractional Sobolev spaces and proves that they are isomorphisms between the corresponding Sobolev space of order α and the \(L_2\)-space. On the basis of such fractional derivatives, he is able to formulate initial value problems for time fractional ordinary differential equations and to prove the well-posedness. For the entire collection see [Zbl 1470.26002].
functional-differential equations with fractional derivatives
scientific article; zbMATH DE number 7388313
scientific article