Initial Value Problems of Linear Equations with the Dzhrbashyan–Nersesyan Derivative in Banach Spaces

Among the many different definitions of fractional derivative, Riemann–Liouville and Gerasimov–Caputo derivatives are most commonly used. In this paper, we consider equations with Dzhrbashyan–Nersesyan which generalizes derivatives; it is transformed into such for two sets parameters that are, in a certain sense, symmetric. The issues unique solvability initial value problems some classes linear inhomogeneous general form derivative Banach spaces investigated. An equation containing bounded operator at considered, solution presented using Mittag–Leffler functions. result obtained made possible to study degenerate case relative p-boundedness pair from equation. Abstract results were used class boundary time-fractional polynomials self-adjoint elliptic differential respect spatial variables.