On well-posed solvability of boundary value problems for equations with fractional derivatives in hyper-weight spaces of continuous functions on

Abstract

In the paper, we establish uniformly well-posed solvability of boundary value problems for equations , in the Banach space where the operator A is a generator of semi-group U(x) of the class with the estimate , , M does not depend on x. The results are applied to the investigation of well-posed solvability of boundary value problems for differential equations with fractional derivatives in weight spaces of continuous functions and investigation of problems of heat-and-mass-transfer and of radio physics.