@article { author = {Haghi, Tahereh and Ghanbari, Kazem}, title = {Positive solutions for discrete fractional initial value problem}, journal = {Computational Methods for Differential Equations}, volume = {4}, number = {4}, pages = {285-297}, year = {2016}, publisher = {University of Tabriz}, issn = {2345-3982}, eissn = {2383-2533}, doi = {}, abstract = {‎‎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.}, keywords = {discrete fractional calculus,existence of solutions,Positive solution‎, ‎Fixed point theorem}, url = {https://cmde.tabrizu.ac.ir/article_5644.html}, eprint = {https://cmde.tabrizu.ac.ir/article_5644_90f2bdba699867d7927f805399e1c7bf.pdf} }