Some novel analyses of the Caputo-type singular three-point fractional boundary value problems

In this article, we consider singular three-point second-order boundary value problems in the sense of the Caputo fractional derivatives. We derive some novel results on the existence of a unique solution for the proposed problems. The problems are numerically solved using the least squares method and neural network scheme. We compare the solutions obtained from both approaches. The fractional-order generalization of the proposed problem, the existence and uniqueness approach, and the numerical solutions are the novel features of this study.