<p>This work focuses on analyzing some physical homogeneous and nonhomogeneous fractional third-order dispersive differential equations (FDEs) using an innovative technique, namely, the Tantawy technique. This technique was recently developed, with its primary attribute being its straightforwardness during application for solving FDEs without any challenges, and it also achieves high accuracy and enhanced stability. It is well known that the family of the fractional KdV equation is widely used to analyze many linear and nonlinear phenomena in fluid mechanics, electronic circuits, and the description of seawater, in addition to its widespread use in plasma physics. From this standpoint, this investigation discusses four models of homogeneous and nonhomogeneous fractional linear KdV-type equations, and derives some approximations to these equations. The derived approximations are analyzed both numerically and graphically to understand the dynamics of the phenomena described by these approximations. Furthermore, the absolute error of all derived approximations is calculated to evaluate the accuracy and efficiency of the used technique. The convergence and reliability of the proposed technique are thoroughly analyzed, demonstrating their capability to handle the complexities of fractional order systems with high accuracy. Numerical experiments confirm the validity and effectiveness of the proposed technique. The obtained results can be utilized to study various physical phenomena occurring in electrical circuits, characterize seawater, and elucidate numerous phenomena in plasma physics.</p>