A coupled system of q-fractional Lane-Emden problem involving three sequential q-fractional derivatives with stability inequality

Abstract In the current manuscript, we consider a sequential q -fractional Lane-Emden system involving Riemann-Liouville and Caputo type fractional q -derivatives. We prove the uniqueness of solutions by means Banach fixed point theorems. Then, to demonstrate theexistence of at least one solution, we use Schaefer's fixed point theorem. Also we define and prove two types of Ulam-Hyers for the proposed system. Finally, an illustrative example is proposed. (2010) Mathematics Subject Classifications: 39A13, 39B72, 30C45.