doi:10.1007/s10543-019-00777-0engGracia, José LuisO’Riordan, EugeneStynes, MartinConvergence analysis of a finite difference scheme for a two-point boundary value problem with a Riemann–Liouville–Caputo fractional derivativeART-2020-118663The Riemann–Liouville–Caputo (RLC) derivative is a new class of derivative that is motivated by modelling considerations; it lies between the more familiar Riemann–Liouville and Caputo derivatives. The present paper studies a two-point boundary value problem on the interval [0,  L] whose highest-order derivative is an RLC derivative of order a¿ (1 , 2). It is shown that the choice of boundary condition at x= 0 strongly influences the regularity of the solution. For the case where the solution lies in C1[0 , L] n Cq + 1(0 , L] for some positive integer q, a finite difference scheme is used to solve the problem numerically on a uniform mesh. In the error analysis of the scheme, the weakly singular behaviour of the solution at x= 0 is taken into account and it is shown that the method is almost first-order convergent. Numerical results are presented to illustrate the performance of the method.2020http://zaguan.unizar.es/record/13078710.1007/s10543-019-00777-0http://zaguan.unizar.es/record/130787oai:zaguan.unizar.es:130787info:eu-repo/grantAgreement/ES/DGA-FSE/E24-17Rinfo:eu-repo/grantAgreement/ES/MCYT-FEDER/MTM2016-75139-Rinfo:eu-repo/grantAgreement/ES/MINECO/MTM2016-75139-RBIT Numerical Mathematics 60, 2 (2020), 411-439All rights reservedhttp://www.europeana.eu/rights/rr-f/info:eu-repo/semantics/openAccess