The present paper investigates the dynamical properties of dust-ion-acoustic solitary waves in a three component plasma system containing inertial thermal ions with weakly relativistic effect, inertialess electrons and negatively charge stationary dust grains. The electrons are assumed to obey the Kaniadakis distribution as governed by a deformation index \(\kappa \) . Utilizing appropriate reductive perturbation approach, the Korteweg–de Vries (KdV) and modified KdV equations are derived from governing equations and the soliton solutions are numerically investigated. The study demonstrates that the KdV equation permits a combination of compressive and rarefactive DIA solitary structures as a result of configuration of parameter, and the mKdV equation allows for the simultaneous presence of compressive and rarefactive solitary structures in the plasma with finite amplitude. The dominance of physical parameters, such as dust concentration \(\mu \) , relativistic factor \(u_0 /c\) , ion temperature \(\sigma \) , and \(\kappa \) -deformed parameter over the dynamics of solitary structure, is thoroughly analyzed in the paper. The implication of the outcomes of this investigation may be admissible for understanding the dynamics of dust-ion-acoustic waves in both space and laboratory plasmas where warm relativistic ions exist.
