In this manuscript, by using the Caputo and Riemann–Liouville type fractional q-derivatives, we consider two fractional q-integro-differential equations of the forms for t ∈ [0, l] under sum and integral boundary value conditions on a time scale Tt0 = {t : t = t0qn} ∪ {0} for n ∈ N where t0 ∈ R and q in (0, 1). By employing the Banach contraction principle, sufficient conditions are established to ensure the existence of solutions for the addressed equations. Examples involving algorithms and illustrated graphs are presented to demonstrate the validity of our theoretical findings.
