Initial value problem for a class of fractional order inhomogeneous equations in Banach spaces

Abstract

Initial value problem for a class of fractional order linear inhomogeneous equations in Banach spaces with a bounded operator at the unknown function is considered. The equation contains the Riemann–Liouville fractional derivative and the corresponding initial conditions are set for the fractional derivatives of a solution. The theorem of the problem unique solvability is proved. It is applied for studying of the solvability of initial boundary value problem for a filtration theory equation with Riemann–Liouville time-fractional order.