In the research work, we discuss a multi-singular pointwise defined fractional $q$–integro-differential equation under some boundary conditions via the Riemann-Liouville $q$–integral and Caputo fractional $q$–derivatives. New existence results rely on the $\alpha$-admissible map and fixed point theorem for $\alpha$- $\mathtt{\psi }$-contraction map. At the end, we present an example with application and some algorithms to illustrate the primary effects.