Positive solutions for discrete fractional initial value problem

Document Type : Research Paper


Sahand University of Technology, Tabriz, Iran


‎‎In this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎The solutions of fractional difference equation are the size of tumor in model tumor growth described by the Gompertz function‎. ‎We use the method of upper and lower solutions and Schauder fixed point theorem to obtain the main results‎.


Volume 4, Issue 4 - Serial Number 4
October 2016
Pages 285-297
  • Receive Date: 06 September 2016
  • Revise Date: 07 January 2017
  • Accept Date: 15 January 2017
  • First Publish Date: 15 January 2017