<p>We presents a robust stability criterion for a non-homogeneous time-fractional diffusion equation involving the regularized Caputo-like counterpart of the hyper-Bessel differential operator. The criterion is obtained by extending the concept of total stability, or stability under constantly acting perturbing forces, that is regularly applied to systems of ordinary differential equations. The criterion allows us to pre-establish a bound for the solutions of the time-fractional partial differential equation, as well as for its time-fractional derivative and its first partial derivative with respect to the longitudinal axis.</p>