Details

Autor(en) / Beteiligte

• Podlubny, Igor
• Skovranek, Tomas
• Vinagre Jara, Blas M.
• Petras, Ivo
• Verbitsky, Viktor
• Chen, YangQuan

Titel

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

Ist Teil von

• Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, 2013-05, Vol.371 (1990), p.20120153-20120153

Ort / Verlag

England: The Royal Society Publishing

Erscheinungsjahr

2013

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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', because it is applied in combination with the matrix approach for each 'large step'. This new method is also illustrated by an easy-to-follow example. The presented approach allows fractional-order and distributed-order differentiation and integration of non-uniformly sampled signals, and opens the way to development of variable- and adaptive-step-length techniques for fractional- and distributed-order differential equations.