Analytic Resolvent Operator and Existence Results for Fractional Integro-Differential Equations

Volume 2, Number 2 (2012), 26 - 47

Analytic Resolvent Operator and Existence Results for Fractional Integro-Differential Equations

Communicated By:
Enrique Zuazua
Price: \$20.00

Abstract

In this paper we study the existence and qualitative properties of an -resolvent operator for an abstract fractional integro-differential problem D t x(t) = Ax(t)+ Z t 0 B(t− s)x(s)ds, t > 0, x(0) = x0, x0(0) = x1, where 2 (1, 2);A, (B(t))t0 are closed linear operators defined on a common domain which is dense in a Banach space X. The existence of mild and classical solutions for the non homogeneous equation is also studied.