Nowadays, many researchers have considerable attention to fractional calculus as a useful tool for modeling of different phenomena in the world. In this work, we investigate the sum-type singular nonlinear fractional q integro-differential equations withm-point boundary value problem. The existence of positive solutions is obtained by the properties of the Green function, standard Caputo q derivative, Riemann–Liouville fractional q integral, and a fixed point theorem on a real Banach space , which has a partial order by using a cone P ⊂ . The proofs are based on solving the operators equation. By providing seven algorithms, four tables, and three figures, we give two numerical examples to illustrate our main result.
