TY - CHAP A1 - Diethelm, Kai ED - Ball, Joseph ED - Tylli, Hans-Olav ED - Virtanen, Jani A. T1 - Shooting methods for fractional Dirichlet-type boundary value problems of order α ∈ (1, 2) with Caputo derivatives T2 - Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis N2 - For the numerical solution of Dirichlet-type boundary value problems associated to nonlinear fractional differential equations of order 𝛼 ∈ (1, 2) that use Caputo derivatives, we suggest to employ shooting methods. In particular, we demonstrate that the so-called proportional secting technique for selecting the required initial values leads to numerical schemes that converge to high accuracy in a very small number of shooting iterations, and we provide an explanation of the analytical background for this favourable numerical behaviour. KW - fractional differential equation KW - Caputo derivative KW - boundary condition KW - boundary value problem KW - shooting method KW - proportional secting KW - secant method Y1 - 2025 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:863-opus-59665 SN - 978-3-032-00154-2 PB - Birkhäuser CY - Cham ER -