Fractional-order (FO) systems are a special subset of linear time-invariant (LTI) systems. The transfer functions (TFs) of these systems are rational functions with polynomials of rational powers of the Laplace variable ‘s’. FO systems are of interest for both controller design and modelling purpose. It has been shown that FOPID controller gives better response as compared to integer-order(IO) controllers. FO systems provide the accurate models for many real systems. The stability analysis of FO systems, which is quite different from that of integer- order(IO) systems analysis, is the main focus of this paper. Stability is defined using Riemann surface because of their multi- valued nature of the FO transfer functions (FOTFs). In this paper, various approaches viz., time domain analysis, frequency domain analysis, state space representation are discussed. Both the types of FO systems, with commensurate and incommensurate TFs, are discussed

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Fractional-order systems fractional calculus stability analysis