Bull. Malays. Math. Sci. Soc. https://doi.org/10.1007/s40840-018-0625-x On Ulam’s Stability for a Coupled Systems of Nonlinear Implicit Fractional Differential Equations Zeeshan Ali 1 · Akbar Zada 1 · Kamal Shah 2 Received: 29 November 2017 / Revised: 31 March 2018 © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018 Abstract In this manuscript, we study the existence, uniqueness and various kinds of Ulam stability including Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability and generalized Ulam–Hyers–Rassias stability of the solutions to a nonlinear coupled systems of implicit fractional differential equations involving Caputo derivative. We develop conditions for uniqueness and existence by using the classical fixed point theorems such as Banach contraction principle and Leray–Schauder of cone type. For stability, we utilize classical functional analysis. Also, an example is given to demonstrate our main theoretical results. Keywords Caputo derivative · Fractional-order differential equation · Coupled system · Green function · Boundary conditions · Ulam stability Mathematics Subject Classification 34A08 · 34B15 · 34B27 Communicated by Norhashidah Hj. Mohd. Ali. B Kamal Shah kamalshah408@gmail.com Zeeshan Ali zeeshanmaths1@gmail.com Akbar Zada zadababo@yahoo.com 1 Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan 2 Department of Mathematics, University of Malakand, Lower Dir, Khyber Pakhtunkhwa, Pakistan 123