TY - JOUR A1 - Diethelm, Kai ED - Altenbach, Holm ED - Öchsner, Andreas T1 - Numerical Methods for the Fractional Differential Equations of Viscoelasticity JF - Encyclopedia of Continuum Mechanics N2 - Mathematical models based on differential operators of fractional order have proven to be very useful for describing the properties of viscoelastic materials. However, the associated differential equations can usually not be solved analytically. In this article, we provide a survey of the most important numerical methods. We restrict our attention to those types of fractional differential equations that are most important in the context of viscoelasticity, i.e., we discuss numerical methods for ordinary fractional differential equations and for certain types of time-fractional partial differential equations. Space-fractional partial differential equations are not discussed. Y1 - 2018 SN - 978-3-662-53605-6 U6 - https://doi.org/10.1007/978-3-662-53605-6_89-1 SP - 1 EP - 12 PB - Springer CY - Berlin ER - TY - JOUR A1 - Diethelm, Kai A1 - Ford, Neville J. T1 - A note on the well-posedness of terminal value problems for fractional differential equations JF - Journal of Integral Equations and Applications N2 - This note is intended to clarify some important points about the well-posedness of terminal value problems for fractional differential equations. It follows the recent publication of a paper by Cong and Tuan in this journal, in which a counter-example calls into question the earlier results in a paper by this note's authors. Here, we show in the light of these new insights, that a wide class of terminal value problems of fractional differential equations is well posed, and we identify those cases where the well-posedness question must be regarded as open. Y1 - 2018 U6 - https://doi.org/10.1216/JIE-2018-30-3-371 VL - 30 IS - 3 SP - 371 EP - 376 ER -