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.
Keywords
nabla fractional derivative, iterative sysytem, boundary value problem, cone, fixed point theorem, Rus’s theoremPersistent identifier
http://hdl.handle.net/11012/207744Document type
Peer reviewedDocument version
Final PDFSource
Mathematics for Applications. 2022 vol. 11, č. 1, s. 57-74. ISSN 1805-3629http://ma.fme.vutbr.cz/archiv/11_1/ma_11_1_khuddush_prasad_final.pdf
Collections
- 2022/1 [7]