Riemann-Liouville Differential and Integral Operators

  • Kai DiethelmEmail author
Part of the Lecture Notes in Mathematics book series (LNM, volume 2004)


This chapter begins with the definition of fractional integral operators in the sense of Riemann and Liouville and with an investigation of their fundamental properties. Based on these integral operators we then introduce the Riemann-Liouville differential operators and discuss their behaviour. Moreover we analyze how the differential operators and the integral operators interact with each other. The chapter is concluded with a brief survey of the Grünwald-Letnikov differential and integral operators and their connection to their counterparts in the sense of Riemann and Liouville.


Differential Operator Integral Operator Fractional Derivative Pointwise Convergence Bernstein Polynomial 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  1. 1.GNS Gesellschaft für Numerische Simulation mbHBraunschweigGermany

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