Continuation and maximal regularity of fractional-order evolution equation

The Cauchy problem of the homogeneous fractional-order evolution equation and evolutionary integral equation have been considered in J. Fract. Calc. 7 (1995) 89] and Korean J. Comput. Appl. Math. 9 (2002) 525]. The existence and uniqueness of the solution have been proved and the continuation of the solution and its fractional order derivative has been proved. Here we study the maximal regularity, continuation and some other properties of the Cauchy problem of the non-homogeneous fractional order evolution equation.