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May 20, 2026MathematicsOpen Access

Inverse Boundary Conditions Interface Problem for Tempered Fractional Ordinary Differential Equations

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Randomized trial identifies boundary conditions in tempered fractional ordinary differential equations, suggesting effective numerical methods.

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.

Koleva et al. (2026) studied this question.

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Randomized trial identifies boundary conditions in tempered fractional ordinary differential equations, suggesting effective numerical methods.