Abstract fractional inverse source problem of order 0 < α < 1 in a Banach space.

Given an abstract Cauchy problem with time-fractional derivative in the Caputo sense of order 0 < α < 1 in a Banach space with an inhomogeneous term φ (t) ϑ , we investigate the inverse problem of determining ϑ from it and an overdetermination in the form of an integral. Assume that the operator of evolution A generates an analytic C 0 -semigroup, we give the uniqueness and unique existence of the solution in terms of the eigenvalues and spectrum of A. And via the approach of functional calculus, the representation of the solution is given. [ABSTRACT FROM AUTHOR]