Abstract
In this chapter we present a general approach to numerical solution to discretization of distributed-order derivatives and integrals, and to numerical solution of ordinary and partial differential equations of distributed order.
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Notes
- 1.
Here due to the use of the descending numbering of discretization nodes the roles of the matrices \(B_n^{(\alpha )}\) (originally for backward fractional differences) and \(F_n^{(\alpha )}\) (originally for forward fractional differences) are swapped in comparison with Podlubny (2000), where these matrices were introduced for the first time. However, we would like to preserve the notation \(B_n^{(\alpha )}\) for the case of the backward fractional differences approximation and \(F_n^{(\alpha )}\) for the case of the forward fractional differences approximation.
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Jiao, Z., Chen, Y., Podlubny, I. (2012). Numerical Solution of Differential Equations of Distributed Order. In: Distributed-Order Dynamic Systems. SpringerBriefs in Electrical and Computer Engineering(). Springer, London. https://doi.org/10.1007/978-1-4471-2852-6_5
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DOI: https://doi.org/10.1007/978-1-4471-2852-6_5
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