Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4631888 | Applied Mathematics and Computation | 2011 | 9 Pages |
Abstract
This paper is concerned with the existence and uniqueness of weighted pseudo almost automorphic mild solution to the semilinear fractional equation: Dtαu(t)=Au(t)+Dtα-1f(t,u(t),Bu(t)),t∈R,1<α<2 where A is a linear densely defined operator of sectorial type on a complex Banach space XX and B is a bounded linear operator defined on XX. Under the assumption of uniformly continuity on f, we establish a composition of weighted pseudo almost automorphic in a general Banach space and obtain existence results by means of Banach contraction mapping. The results obtained are utilized to study the existence and uniqueness of a weighted pseudo almost automorphic solution to fractional diffusion wave equation with Dirichlet conditions.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Gisèle M. Mophou,