Regularity for Fractional Order Retarded Neutral Differential Equations in Hilbert Spaces

Abstract

Abstract. In this paper, we study the existence of solutions and L 2 -regularity for fractional order retarded neutral functional differential equations in Hilbert spaces. We no longer require the compactness of structural operators to prove the existence of continuous solutions of the nonlinear differential system, but instead we investigate the relation between the regularity of solutions of fractional order retarded neutral functional differential systems with unbounded principal operators and that of its corresponding linear system excluded by the nonlinear term. Finally, we give a simple example to which our main result can be applied.

Controllability for Retarded Semilinear Neutral Control Systems of Fractional Order in Hilbert Spaces

“…By virtue of Theorem 2.1 of[23], we have the following result on the corresponding linear equation of (8).…”