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We introduce a new family of fractional convolution quadratures based on generalized Adams methods for the numerical solution of fractional differential equations. We discuss their accuracy and linear stability properties. The boundary loci reported show that, when used as Boundary Value Methods, these schemes overcome the classical order barrier for A-stable methods. [ABSTRACT FROM AUTHOR]

General Linear Methods were introduced in order to encompass a large family of numerical methods for the solution of ODE-IVPs, ranging from LMF to RK formulae. In so doing, it is possible to obtain methods able to overcome typical drawbacks of the previous classes of methods. For example, stability limitations of LMF and order reduction for RK methods. Nevertheless, these goals are usually achieved at the price of a higher computational cost. Consequently, many efforts have been done in order to derive GLMs with particular features, to be exploited for their efficient implementation. In recent years, the derivation of GLMs from particular Boundary Value Methods (BVMs), namely the family of Generalized BDF (GBDF), has been proposed for the numerical solution of stiff ODE-IVPs. Here, this approach is further developed in order to derive GLMs combining good stability and accuracy properties with the possibility of efficiently solving the generated discrete problems via the blended implementation of the methods. [ABSTRACT FROM AUTHOR]