On strong solutions for a class of semilinear fractional degenerate evolution equations with lower fractional derivatives

Abstract

The existence of a unique strong solution on a given interval is proved for the generalized Showalter–Sidorov problem to a class of semilinear fractional degenerate evolution equations in Banach spaces. Nonlinearity is assumed to be dependent on lower order fractional derivatives. All fractional derivatives are understood in the sense of Gerasimov–Caputo. The obtained abstract result is applied to study an initial‐boundary value problem to a modified Sobolev system of equations of the motion of rotated stratified fluid, which is perturbed by a nonlinearity depending on a lower fractional derivative, and a class of initial‐boundary value problems to the semilinear time‐fractional equation with polynomials of an elliptic self‐adjoint differential with respect to spatial variables operator as linear operators in the considered above abstract equation.