Inverse problems for evolution equations with fractional integrals at boundary-value conditions

Abstract

The following problem is considered: to find a solution and a term of a first-order differential equation in a Banach space if the initial-value condition and an excessive condition containing the fractional Riemann-Liouville integral are given. We show that the solvability of the considered problem depends on the distributions of zeroes of the Mittag-Leffler function.