Attractivity of solution with compact and non-compact semigroups for fractional evolution equation

Resumo

We start the problem of atractivity of solutions for fractional evolution equation. We obtain some interesting results of mild solution for fractional evolution system with order _ 2 (1; 2) in Banach space. There was a lot of circumstances for existence of universal attractive solution. We explain the Cauchy problems in these cases for which the semi-group is compact as well as non compact. Our results basically show some features of solution. We proceed the new representation of solution operators, by Laplace heat (is the new concept of light solution for objective equation), and Mainardi’s Wright-type function then we go ahead to set up a new compact solution operators that contract results at the point when the sine family is compact.