Uniqueness Analysis of Boundary Value Problems with Variable-order Caputo Fractional Derivatives
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Abstract
This work is devoted to a boundary value problem for variable-order Caputo fractional derivatives. The obtained conditions guarantee the uniqueness of solutions under given boundary conditions. The main tool in the analysis is the Banach contraction principle, with which one can assert that the problem admits exactly one solution. A numerical example is also presented for illustration and confirmation of the theoretical results.
MSC 2020: 26A30; 34A12; 34K37; 65 L 03
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Copyright (c) 2025 Gunasekar T, et al.
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