Matrix approach to discrete fractional calculus III: non-equidistant grids, variable step length and distributed orders

@article{Podlubny2013MatrixAT,
  title={Matrix approach to discrete fractional calculus III: non-equidistant grids, variable step length and distributed orders},
  author={Igor Podlubny and Tomas Skovranek and Blas M Vinagre Jara and Ivo Petr{\'a}{\vs} and V. G. Verbitsky and Yang Quan Chen},
  journal={Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences},
  year={2013},
  volume={371}
}
  • I. Podlubny, T. Skovranek, Y. Chen
  • Published 13 May 2013
  • Mathematics, Computer Science
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
In this paper, we further develop Podlubny’s matrix approach to discretization of integrals and derivatives of non-integer order. Numerical integration and differentiation on non-equidistant grids is introduced and illustrated by several examples of numerical solution of differential equations with fractional derivatives of constant orders and with distributed-order derivatives. In this paper, for the first time, we present a variable-step-length approach that we call ‘the method of large steps… 
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SuntoSi generalizza la soluzione di equazioni differenziali di ordine frazionario al caso in cui le derivate frazionarie sono integrate rispetto all’ordine di differenziazione. La soluzione formale è
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