Time-Dependent Source Identification Problem for Fractional Schrodinger Type Equations

The time-dependent source identication problem for the Schrödinger equation of fractional order ( , ), , 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. A list of examples of operator and functional is discussed, including linear systems of fractional differential equations, differential models with involution, fractional Sturm–Liouville operators, and others.