Existence results for impulsive fractional q-difference equations with anti-periodic boundary conditions

Bashir Ahmad, Jessada Tariboon, Sotiris K Ntouyas, Hamed H Alsulami, Shatha Monaquel
2016 Boundary Value Problems  
This paper studies a Caputo type anti-periodic boundary value problem of impulsive fractional q-difference equations involving a q-shifting operator of the form a q (m) = qm + (1 -q)a. Concerning the existence of solutions for the given problem, two theorems are proved via Schauder's fixed point theorem and the Leray-Schauder nonlinear alternative, while the uniqueness of solutions is established by means of Banach's contraction mapping principle. Finally, we discuss some examples illustrating the main results.
doi:10.1186/s13661-016-0521-y fatcat:pwdng6qerbebfmsn2eeftpvqbu