This paper is concerned with the existence of positive solutions of three classes of nonlinear fractional differential equations using fixed point results in non-zero self-distance spaces. We introduce new concepts of generalized α-weakly ( ψ φ ) s -contractive mappings involving rational terms and then develop fixed point results for weakly α-admissible mappings. Some new examples and counterexamples are given to illustrate the applicability and effectiveness of these results over existing ones. In that way, we extend some previous results. For applications to fractional q-difference boundary value problems, the use of a p-Laplacian operator is suggested. © 2017 Walter de Gruyter GmbH, Berlin/Boston 2017.