Existence and Ulam's type stability results for a class of fractional boundary value problems on a star graph

Abstract

This paper is concerned with a nonlinear fractional boundary value problem on a star graph. By using a transformation, the suggested problem is converted into an equivalent system of fractional boundary value problem. Schaefer's fixed point theorem and Banach's contraction principle is used to establish its existence and uniqueness results. Further, different kinds of Ulam's type stability results for the proposed problem have been discussed. Finally, two examples are presented to illustrate the application of the obtained results.