Existence of almost periodic solution for nonlocal fractional Cauchy problem with integral initial condition

S. Maghsoodi, A. Neamaty

In this research, we intend to show that the nonlocal fractional Cauchy problem Dαu(t)=A(t)u(t)+f(t,u(t)), t∈J=[0,1] with integral initial condition u(0)=∫01g(s,u(s))ds, in the Banach space X, where A is a generator of α-resolvent operator function {T(t)}t≥0 and f, g are given functions satisfying some assumptions, has an almost periodic solution. 

Tbilisi Mathematical Journal, Vol. 14(3) (2021), pp. 163-170