Fractional calculus and fractional order operators

  • Sabir Umarov
Part of the Developments in Mathematics book series (DEVM, volume 41)


Fractional order differential equations are an efficient tool to model various processes arising in science and engineering. Fractional models adequately reflect subtle internal properties, such as memory or hereditary properties, of complex processes that the classical integer order models neglect. In this chapter we will discuss the theoretical background of fractional modeling, that is the fractional calculus, including recent developments - distributed and variable fractional order differential operators.


Variable-order Fractional Derivatives Fractional Order Differential Equations Fractional Order Integral Operator Marchaud Riemann Liouville Derivative 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sabir Umarov
    • 1
  1. 1.Department of MathematicsUniversity of New HavenWest HavenUSA

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