Initial value problems for some classes of linear evolution equations with several fractional derivatives

The problems of unique solvability initial for linear inhomogeneous equations a general form with several Gerasimov-Caputo fractional derivatives in Banach spaces are investigated. Cauchy problem is considered an equation solved respect to the highest derivative containing bounded operators at lowest derivatives. solution presented use Dunford-Taylor type integrals. obtained result allowed us study degenerate operator derivative, provided that, this operator, second largest 0-bounded. Abstract results applied class initial-boundary value time and polynomials self-adjoint elliptic differential space variables.