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Mathematics
Volume 14
Issue 10
10.3390/math14101711
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Article

Inverse Boundary Conditions Interface Problem for Tempered Fractional Ordinary Differential Equations

by
Miglena N. Koleva
1,* and
Lubin G. Vulkov
2,*
1
Department of Mathematics, Faculty of Natural Sciences and Education, University of Ruse “Angel Kanchev”, 8 Studentska Str., 7017 Ruse, Bulgaria
2
Department of Applied Mathematics and Statistics, Faculty of Natural Sciences and Education, University of Ruse “Angel Kanchev”, 8 Studentska Str., 7017 Ruse, Bulgaria
*
Authors to whom correspondence should be addressed.
Mathematics 2026, 14(10), 1711; https://doi.org/10.3390/math14101711 (registering DOI)
Submission received: 17 April 2026 / Revised: 13 May 2026 / Accepted: 14 May 2026 / Published: 16 May 2026
(This article belongs to the Special Issue Advanced Numerical and Computational Methods for Engineering and Applied Mathematical Problems, 2nd Edition)
Versions Notes

Abstract

This paper focuses on the identification of boundary conditions in tempered fractional ordinary differential equations interface problem on disjoint intervals based on point observations (measurements). First, we discuss some properties of tempered fractional calculus, including fractional integration by parts in appropriate Sobolev spaces. Then, after formulating the direct and inverse problems, we establish the well-posedness of a tempered fractional boundary-value problem on disjoint intervals. Two numerical methods for solving the inverse problem of determining the external boundary conditions are proposed, and their correctness is studied. Finally, numerical experiments are presented to demonstrate the efficiency of the proposed approaches.
Keywords: tempered fractional ordinary differential equation; disjoint domain; inverse interface problem; point observation; decomposition; finite difference method tempered fractional ordinary differential equation; disjoint domain; inverse interface problem; point observation; decomposition; finite difference method

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MDPI and ACS Style

Koleva, M.N.; Vulkov, L.G. Inverse Boundary Conditions Interface Problem for Tempered Fractional Ordinary Differential Equations. Mathematics 2026, 14, 1711. https://doi.org/10.3390/math14101711

AMA Style

Koleva MN, Vulkov LG. Inverse Boundary Conditions Interface Problem for Tempered Fractional Ordinary Differential Equations. Mathematics. 2026; 14(10):1711. https://doi.org/10.3390/math14101711

Chicago/Turabian Style

Koleva, Miglena N., and Lubin G. Vulkov. 2026. "Inverse Boundary Conditions Interface Problem for Tempered Fractional Ordinary Differential Equations" Mathematics 14, no. 10: 1711. https://doi.org/10.3390/math14101711

APA Style

Koleva, M. N., & Vulkov, L. G. (2026). Inverse Boundary Conditions Interface Problem for Tempered Fractional Ordinary Differential Equations. Mathematics, 14(10), 1711. https://doi.org/10.3390/math14101711

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