Analytic resolving families of operators for equations with discretely distributed fractional derivative

Abstract

Analytic resolving families of operators for equations with discretely distributed fractional derivative We study the unique solvability of linear equations in Banach spaces with a discretely distributed Gerasimov -Caputo fractional derivative in terms of analytic resolving families of operators. Necessary and sufficient conditions for the existence of such a family of operators are obtained in terms of the resolvent of a closed operator from the right side of the equation, and their properties are studied. These results are used to prove the existence of a unique solution to the Cauchy problem for a linear inhomogeneous equation of the corresponding class.