\(S\)-asymptotically \(\omega \)-periodic solutions of semilinear fractional integro-differential equations
The authors consider the following semilinear fractional integro-differential equation \[ v'(t) = \int_0^t \frac{(t - s)^{\alpha - 2}}{\Gamma (\alpha - 1)} Av(s)\,ds + f(t,v(t)), \quad t \geq 0, \quad v(0) = u_0 \in X, \] where \(1 < \alpha < 2\), \(A:D(A) \subset X \to X\) is a linear densely defined operator of sectorial type on a complex Banach space \(X\), and \(f:[0,\infty )\times X \to X\) is a continuous function satisfying a suitable Lipschitz type condition. The existence and uniqueness of an \(S\)-asymptotically \(\omega\)-periodic mild solution to this problem is obtained.
\(S\)-asymptotically \(\omega\)-periodic function
semilinear integro-differential equations
scientific article; zbMATH DE number 5563910
scientific article