University of Tabriz Computational Methods for Differential Equations 2345-3982 4 4 2016 10 01 Positive solutions for discrete fractional initial value problem 285 297 5644 EN Tahereh Haghi Sahand University of Technology, Tabriz, Iran Kazem Ghanbari Sahand University of Technology, Tabriz, Iran Journal Article 2016 09 06 ‎‎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. discrete fractional calculus existence of solutions Positive solution‎, ‎Fixed point theorem https://cmde.tabrizu.ac.ir/article_5644_90f2bdba699867d7927f805399e1c7bf.pdf