Iterative system of nabla fractional difference equations with two-point boundary conditions

Abstract

In this paper, we consider the nabla fractional order boundary value prob- lem ∇ß−1 n0 [∇zj (t)] + φ(t)gj (zj+1(t)) = 0, t ∈ Nn n0+2, 1 < ß < 2, azj (n0 + 1) − b∇zj (n0 + 1) = 0, czj (n) + d∇zj (n) = 0, where j = 1, 2, . . . , N , zN +1 = z1, N ∈ N, n0, n ∈ R with n − n0 ∈ N and de- rive sufficient conditions for the existence of positive solutions by an application of Krasnoselskii’s fixed point theorem on a Banach space. Later, we derive suffi- cient conditions for the existence of a unique solution by applying Rus’s contraction mapping theorem in a metric space, where two metrics are employed.