A hybrid kernel functions collocation approach for boundary value problems with Caputo fractional derivative

In the work of Rosenfeld et al. (2017), Mittag-Leffler RKHS was introduced and kernelized ABM was presented to solve initial value problems with Caputo fractional derivative. However, the stability of the method is unsatisfactory. In this letter, combining advantages of the Sobolev and Mittag-Leffler kernel functions, we will develop a hybrid kernel functions collocation approach for boundary value problems with Caputo fractional derivative. The approach can improve the stability of the Mittag-Leffler kernel function based method and the accuracy of the Sobolev kernel function based technique for Caputo fractional problems.(c) 2023 Elsevier Ltd. All rights reserved.