Well-posedness of Riemann-Liouville fractional degenerate equations with finite delay in Banach spaces

Abstract

We study the Existence and uniqueness of solutions of the Riemann-Liouville fractional integrodifferential degenerate equations

$\frac{d}{dt}(B \frac{1}{\Gamma (1 - \alpha)}\int_{- \infty}^{t}(t - s)^{- \alpha } x(s) ds )= Ax(t) + \int_{-\infty}^{t}a(t -s)x(s)ds + L(x_{t}) + \frac{1}{\Gamma (\beta)} \int_{- \infty}^{t}(t - s)^{\beta - 1 } x(s) ds + f(t)$.

where A and B are a linear closed operators in a Banach space.