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Positive solutions for a system of nonlinear semipositone fractional \(q\)-difference equations with \(q\)-integral boundary conditions Positive solutions for a system of nonlinear semipositone fractional \(q\)-difference equations with \(q\)-integral boundary conditions en en In this paper, by virtue of fixed point index on cones, we obtain two existence theorems of positive solutions for a system of nonlinear semipositone fractional \(q\)-difference equations with \(q\)-integral boundary conditions. Concave functions and nonnegative matrices are used to characterize the coupling behavior of our nonlinearities. 4430 4440 Wei Cheng School of Mathematical Sciences Chongqing Normal University China 1375415619@qq.com Jiafa Xu School of Mathematical Sciences Chongqing Normal University China xujiafa292@sina.com Yujun Cui State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province Ministry of Science and Technology Shandong University of Science and Technology China China cyj720201@163.com q-difference equation q-integral boundary conditions fixed point index positive solution concave function. Article.35.pdf  R. P. Agarwal, Certain fractional q-integrals and q-derivatives, Proc. Cambridge Philos. Soc., 66 (1969), 365-370 ## Y. Cui, Y. Zou, An existence and uniqueness theorem for a second order nonlinear system with coupled integral boundary value conditions, Appl. Math. Comput., 256 (2015), 438-444 ## R. Dahal, D. Duncan, C. S. 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