This research aims to identify boundary conditions in tempered fractional ordinary differential equations on disjoint intervals using point observations.
Discussed properties of tempered fractional calculus and fractional integration in Sobolev spaces.
Formulated direct and inverse problems, establishing the well-posedness of boundary-value problems on disjoint intervals.
Proposed two numerical methods for solving the inverse problem to determine external boundary conditions.
Numerical experiments show the efficiency of the proposed methods for identifying boundary conditions.
Well-posedness of the problem was established, ensuring reliable solutions for given conditions.