Abstract
The maximal regularity and continuation of the solution (and its fractional-order derivative) of the Cauchy problem of the non-homogeneous fractional order evolution equation D α u(t) = Au(t) + f(t), α ∈ (0,1) have been studied in [A.M.A. El-Sayed and Mohamed. A.E. Herzallah (2004). Continuation and maximal regularity of fractional-order evolution equation. Journal of Mathematical Analysis and Applications, 296 Equation(1), 340–350.]. Here we study the maximal regularity, continuation of the solution (and its fractional derivative), and some other properties of the solution of the Cauchy problem of the non-homogeneous arbitrary (fractional) order evolutionary integral equation.