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Differentiation of Solutions of Caputo Boundary Value Problems with respect to Boundary Data
Version 1
: Received: 14 May 2024 / Approved: 15 May 2024 / Online: 15 May 2024 (07:45:48 CEST)
A peer-reviewed article of this Preprint also exists.
Lyons, J.W. Differentiation of Solutions of Caputo Boundary Value Problems with Respect to Boundary Data. Mathematics 2024, 12, 1790. Lyons, J.W. Differentiation of Solutions of Caputo Boundary Value Problems with Respect to Boundary Data. Mathematics 2024, 12, 1790.
Abstract
Under suitable continuity and uniqueness conditions, solutions of an α order Caputo fractional boundary value problem are differentiated with respect to boundary values and boundary points. This extends well-known results for nth order boundary value problems. The approach used is a standard technique and makes heavy use of recent results for differentiation of solutions of Caputo fractional intial value problems with respect to initial conditions and continuous dependence for Caputo fractional boundary value problems.
Keywords
continuous dependence; Caputo fractional derivative; fractional differential equation; variational equation
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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