Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6420461 | Applied Mathematics and Computation | 2015 | 10 Pages |
Abstract
Given a closed linear operator A in a Banach space X and a multi-valued function with convex, closed values F:[0,b]ÃC([-Ï,0];X)â2X, we consider the Cauchy problemcDtαu(t)âAu(t)+F(t,ut),tâ[0,b],u(t)=Ï(t),tâ[-Ï,0],where Ï⩾0,cDtα,0<α<1, represents the regularized Caputo fractional derivative of order α. We concentrate on the case when the semigroup generated by A is noncompact and obtain nonemptyness of the solution set if, in particular, X is reflexive and F is weakly upper semicontinuous with respect to the second variable. Furthermore, in this situation topological properties of the set of all solutions are considered.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Rong-Nian Wang, Qing-Hua Ma,