<abstract><p>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 $ α $-admissible map and fixed point theorem for $ α $-$ \mathtt{ψ} $-contraction map. At the end, we present an example with application and some algorithms to illustrate the primary effects.</p></abstract>