Journal of the
Korean Mathematical Society JKMS

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.

Keywords: fractional differential equation, retarded system, regularity, analytic semigroup, fractional power

MSC numbers: Primary 35B37; Secondary 35R11