Stability of the time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative

Abstract

The telegraph equation , in a Hilbert space is investigated. Here is a self-adjoint, positive operator, is the Caputo derivative. An inverse problem is considered in which, along with , also a time varying factor of the source function is unknown. To solve this inverse problem, we take the additional condition with an arbitrary bounded linear functional .Existence and uniqueness theorem for the solution to the problem under consideration is proved. Inequalities of stability are obtained.