Differentiation of Solutions of Caputo Boundary Value Problems with Respect to Boundary Data

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 applies a standard al...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-06, Vol.12 (12), p.1790
Main Author: Lyons, Jeffrey W.
Format: Article
Language:English
Subjects:
Algorithms
Analysis
Boundary conditions
boundary value problem
Boundary value problems
Calculus, Differential
Caputo fractional differential equation
continuous dependence
Differentiation
Functions, Continuous
Hypotheses
Initial conditions
Tests, problems and exercises
variational equation
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Summary: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 applies a standard algorithm to achieve the result 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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12121790