A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a Solution
https://doi.org/10.18255/1818-1015-2016-3-370-376
Abstract
A two-point boundary value problem on the interval [0, 1] is considered, where the highest-order derivative is a Caputo fractional derivative of order 2 − δ with 0 < δ < 1. A necessary and sufficient condition for existence and uniqueness of a solution u is derived. For this solution the derivative uŐ is absolutely continuous on [0, 1]. It is shown that if one assumes more regularity — that u lies in C2[0, 1] — then this places a subtle restriction on the data of the problem.
About the Author
M. Stynes
Beijing Computational Science Research Center, Haidian District, Beijing 100193, China
Russian Federation
Russian Federation
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Review
For citations:
Stynes M. A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a Solution. Modeling and Analysis of Information Systems. 2016;23(3):370-376. https://doi.org/10.18255/1818-1015-2016-3-370-376
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