This paper studies linear piecewise fractional delay systems motivated by models with switching dynamics and memory e ects. An explicit interval-wise solution is constructed via a generating-function approach, and its continuity at all junction points is established. Based on this representation, a computable finite-time stability condition is derived in the form of an explicit inequality involving the system parameters, delay, and fractional order. Several scalar and matrix-valued examples illustrate the theoretical results and confirm the effectiveness of the proposed stability criterion. The novelty of this work lies in providing, to the best of our knowledge, the frst explicit interval-wise solution framework for piecewise fractional delay systems together with a directly verifiable finite-time stability condition, thereby extending existing results that rely on implicit formulations or restrictive structural assumptions.