Exact A(α)-Stability Angles for Fractional Linear Multi-step Methods⁎⁎This paper is an output of self curiosity of the authors on the stability angle presented in the seminar series in FracDiff Research Group, Department of Mathemetics, Sultan Qaboos University.

A new criterion for evaluating exact values for the maximum angles of A(α)-stability for linear multistep methods is proposed. This criterion gives an equation to be solved for a complex point corresponding to the tangent line from the origin to the root locus curve of the stability boundary. The maximum angle for A(α)-stability sector is then obtained from the tangent point. This criterion is applied to find the A(α)-stability angles for several fractional backward difference formula type (BDF-type) numerical methods for fractional initial value problems.