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 s...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2022-02, Vol.43 (2), p.303-315
Main Authors: Ashurov, R. R., Shakarova, M. D.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Differential equations
Existence theorems
Fractional calculus
Geometry
Hilbert space
Inverse problems
Linear systems
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Probability Theory and Stochastic Processes
Schrodinger equation
Time dependence
Uniqueness theorems
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Summary: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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080222050055