In this study, by using the Caputo type q–derivative and the Riemann-Liouville type fractional q–derivative, we investigate a multi-singular pointwise defined fractional q–integro-differential equation under some boundary conditions on a time scale. New existence results rely on $\alpha$-admissible map and the fixed point theorem for $\alpha$-$\psi$-contraction map. Lastly, we present an example with application and some algorithms illustrate the primary effects.
