Well‐posedness of degenerate fractional differential equations with finite delay in complex Banach spaces

Abstract

AbstractWe study the well‐posedness of the degenerate fractional differential equations with finite delay: on Lebesgue–Bochner spaces and periodic Besov spaces , where and are closed linear operators in a complex Banach space satisfying , and are fixed, when , and the delay operator is a bounded linear operator from (resp. ) into . Using known operator‐valued Fourier multiplier theorems on and , we completely characterize the ‐well‐posedness and the ‐well‐posedness of above equations. We also give concrete examples that our abstract results may be applied.