Mediterranean Journal of Mathematics

, Volume 12, Issue 1, pp 219–244 | Cite as

Exponential Quadrature Rules for Linear Fractional Differential Equations

  • Roberto Garrappa
  • Marina PopolizioEmail author


This paper focuses on the numerical solution of initial value problems for fractional differential equations of linear type. The approach we propose grounds on expressing the solution in terms of some integral weighted by a generalized Mittag–Leffler function. Then, suitable quadrature rules are devised and order conditions of algebraic type are derived. Theoretical findings are validated by means of numerical experiments and the effectiveness of the proposed approach is illustrated by means of comparisons with other standard methods.

Mathematics Subject Classification (2010)

Primary 65L05 Secondary 26A33 


Fractional differential equation linear problem quadrature rules Mittag–Leffler function accuracy 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità degli Studi di BariBariItaly
  2. 2.Dipartimento di Matematica e Fisica “Ennio De Giorgi”Università del SalentoLecceItaly

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