<p>This paper investigates the order-dependent stability analysis of fractional-order systems subject to time-varying uncertainties structured in the form <i>EF(t)D</i>, where <i>F(t)</i> is a diagonal matrix. Time-varying uncertainties are typically analyzed using Lyapunov-based or Small-Gain-based methods. While Lyapunov-based approaches often lead to stability conditions that are independent of the system's order, small-gain methods tend to be highly conservative. This conservatism mainly arises from the common assumption that the norm of <i>F(t)</i> is bounded, which neglects the diagonal structure of the uncertainty matrix and enlarges the uncertainty set. To address this limitation, an extended Small-Gain-based framework is proposed, incorporating the properties of <i>M</i>-matrices to directly exploit the diagonal structure of <i>F(t)</i> without assuming norm boundedness. The resulting stability conditions are order-dependent and can be expressed in terms of the <i>H</i>_<i>∞</i>-norm within a systematic, LMI-based framework. Two LMI-based approaches are proposed: one formulated as an optimization problem, and the other as a non-optimization condition based on more restrictive assumptions. A numerical example is presented to demonstrate that the proposed method eliminates the conservatism typically observed in conventional approaches that rely on bounding the norm of <i>F(t)</i>. Furthermore, another example illustrates the application of the proposed method to determining the stability region of a fractional-order tumor model.</p>