@inproceedings{Diethelm, author = {Diethelm, Kai}, title = {Shooting methods for fractional Dirichlet-type boundary value problems of order α ∈ (1, 2) with Caputo derivatives}, series = {Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis}, booktitle = {Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis}, editor = {Ball, Joseph and Tylli, Hans-Olav and Virtanen, Jani A.}, publisher = {Birkh{\"a}user}, address = {Cham}, isbn = {978-3-032-00154-2}, doi = {10.1007/978-3-032-00155-9_8}, url = {http://nbn-resolving.de/urn:nbn:de:bvb:863-opus-59665}, abstract = {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.}, language = {en} }