Int. J. Appl. Comput. Math DOI 10.1007/s40819-017-0375-8 ORIGINAL PAPER Existence and Stability Analysis of Three Point Boundary Value Problem Zeeshan Ali 1 · Akbar Zada 1 · Kamal Shah 2 © Springer (India) Private Ltd. 2017 Abstract In this research article, we study the existence and uniqueness of solution for a three points boundary value problem of fractional order differential equations. Further, we also investigate different kinds of Ulam stability such as Ulam-Hyers (UH) stability, gen- eralized Ulam-Hyers (GUH) stability, Ulam-Hyers-Rassias (UHR) stability and generalized Ulam-Hyers-Rassias (GUHR) stability for the proposed problem. The concerned analysis is carried out via using classical technique of nonlinear functional analysis. The main results are demonstrated by providing couple of examples. Keywords Caputo fractional derivative · Boundary conditions · Green function · Fixed point theorem · (UH) stability Mathematics Subject Classification 26A33 · 34A08 · 34B27 Introduction In the course of the most recent decades, fractional calculus has got great attention from the researchers. It has numerous applications in different branches of science, engineering and technology. In fact, (FDEs) describe many real world phenomena and process of dynamics, biology, signal and image processing, cosmology, physics, chemistry etc, with more reliable B Zeeshan Ali zeeshanmaths1@gmail.com Akbar Zada zadababo@yahoo.com Kamal Shah kamalshah408@gmail.com 1 Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan 2 Department of Mathematics, University of Malakand, Chakdara Dir(L), Khyber Pakhtunkhwa, Pakistan 123