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In this study, we delve into the examination of Finite Time Stability (FTS) within a specific class of Fractional-Order Systems (FOS) with time delays. By applying a fixed-point theorem, we establish novel sufficient conditions to ensure FTS for time-delayed FOS within  <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo><</mo><mi>σ</mi><mo><</mo><mn>2</mn></mrow></semantics></math></inline-formula>. Moreover, we investigate the existence and uniqueness of global solutions for this particular system. To demonstrate the credibility of our results, we substantiate our findings through the presentation of two illustrative examples.