Well‐posedness of degenerate fractional integro‐differential equations in vector‐valued functional spaces

Abstract

AbstractWe study the well‐posedness of the fractional degenerate integro‐differential equations in Lebesgue–Bochner spaces and Besov spaces , where A, B and M are closed linear operators on a Banach space X satisfying , , and . We completely characterize the well‐posedness of in the above vector‐valued function spaces on by using operator‐valued Fourier multiplier. We also give an example that our abstract results may be applied.