Time-Dependent Source Identification Problem for Fractional Schrodinger Type Equations

Abstract

Abstract: The time-dependent source identication problem for the Schrödinger equation of fractional order (Formula Presented.), in a Hilbert space H is investigated. Here A is a self-adjoint positive operator, (Formula Presented.) is the Caputo derivative. An inverse problem is considered in which, along with u(t), also a time varying factor p(t) of the source function is unknown. To solve this inverse problem, we take the additional condition (Formula Presented.) with an arbitrary bounded linear functional B. 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 A and functional B is discussed, including linear systems of fractional differential equations, differential models with involution, fractional Sturm–Liouville operators, and others.