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