Ulam stability of solutions of a discrete boundary value problem with fractional order

In this present work, we investigate Ulam - Hyers stability for the following nonlinear discrete fractional order boundary value problem of the form 0 C Δ k δ υ ( k ) = ψ ( k + δ − 1 , υ ( k + δ − 1 ) ) , for k ∈ [ 0 , L ] N 0 = { 0 , 1 , … , L } , with boundary conditions υ ( δ − 2 ) = 0 = υ ( δ + L ) , where ψ : [ δ − 1 , δ + L ] N δ − 1 × R → R is a continuous and 0 C Δ k δ is the Caputo fractional difference operator with 1 < δ ≤ 2.