Premium
On positive solutions to fractional sum boundary value problems for nonlinear fractional difference equations
Author(s) -
Reunsumrit Jiraporn,
Sitthiwirattham Thanin
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3725
Subject(s) - mathematics , fixed point theorem , uniqueness , boundary value problem , nonlinear system , mathematical analysis , picard–lindelöf theorem , banach fixed point theorem , fractional calculus , class (philosophy) , physics , quantum mechanics , artificial intelligence , computer science
In this paper, we study a new class of 3‐point boundary value problems of nonlinear fractional difference equations. Our problems contain difference and fractional sum boundary conditions. Existence and uniqueness of solutions are proved by using the Banach fixed‐point theorem, and existence of the positive solutions is proved by using the Krasnoselskii's fixed‐point theorem. Copyright © 2015 John Wiley & Sons, Ltd.