Premium
Well‐posedness of fractional integro‐differential equations in vector‐valued functional spaces
Author(s) -
Bu Shangquan,
Cai Gang
Publication year - 2019
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201800104
Subject(s) - mathematics , lp space , multiplier (economics) , banach space , function space , pure mathematics , mathematical analysis , fractional calculus , besov space , lebesgue integration , interpolation space , functional analysis , biochemistry , chemistry , gene , economics , macroeconomics
We study the well‐posedness of the fractional differential equations with infinite delay( P α ) :D α u ( t )=A u ( t ) + ∫ − ∞ t a ( t − s ) A u ( s )d s+∫ − ∞ t b ( t − s ) B u ( s )d s + f ( t ) ,( 0 ≤ t ≤ 2 π ) ,on Lebesgue–Bochner spacesL p ( T ; X )and Besov spacesB p , q s ( T ; X ) , where A and B are closed linear operators on a Banach space X satisfying D ( A ) ∩ D ( B ) ≠ { 0 } , α > 0 and a , b ∈ L 1 ( R + ) . Under suitable assumptions on the kernels a and b , we completely characterize the well‐posedness of ( P α ) in the above vector‐valued function spaces on T by using known operator‐valued Fourier multiplier theorems. We also give concrete examples where our abstract results may be applied.