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

Abstract

We study the well-posedness of the fractional differential equations with infinite delayon Lebesgue-Bochner spaces ( ; ) and Besov spaces , ( ; ), where and are closed linear operators on a Banach space satisfying ( ) ∩ ( ) ≠ {0}, > 0 and , ∈ 1 (ℝ + ). Under suitable assumptions on the kernels and , we completely characterize the well-posedness of ( ) in the above vector-valued function spaces on by using known operator-valued Fourier multiplier theorems. We also give concrete examples where our abstract results may be applied. K E Y W O R D SFourier multiplier, fractional differential equation, vector-valued function spaces, well-posedness M S C ( 2 0 1 0 ) 26A33, 34C25, 34K37, 43A15, 45N05

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

“…Our results generalize the previous known results in the simpler case when obtained in [6]. Thus our results also recover the results obtained in [2, 3, 5, 9].…”