Premium
On S ‐asymptotically ω ‐periodic and Bloch periodic mild solutions to some fractional differential equations in abstract spaces
Author(s) -
OueamaGuengai Enock R.,
N'Guérékata Gaston M.
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5062
Subject(s) - mathematics , uniqueness , bounded function , banach space , resolvent , almost periodic function , mathematical analysis , context (archaeology) , fractional calculus , pure mathematics , biology , paleontology
We are concerned with the existence and uniqueness of S ‐asymptotically ω ‐periodic and Bloch periodic mild solutions to the semilinear fractional differential equation of the formD t α u ( t ) = A u ( t ) + f ( t , u ( t ) ) whereD t αis the Riemann‐Liouville derivative, 1 < α < 2 and A is a (generally unbounded) linear operator, which generates a bounded α ‐resolvent family T α ( t ) on a (complex) Banach space X . We use some classical fixed‐point theorems to reach our results. The results are new even in the context of asymptotically periodic solutions.