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Polish Information Processing Society
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Annals of Computer Science and Information Systems, Volume 2

Proceedings of the 2014 Federated Conference on Computer Science and Information Systems

Accuracy Evaluation of Classical Integer Order Based and Direct Non-integer Order Numerical Algorithms of Non-integer Order Derivatives and Integrals Computations

Dariusz W. Brzeziński, Piotr Ostalczyk

DOI: http://dx.doi.org/10.15439/2014F190

Citation: Proceedings of the 2014 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 2, pages 553–560 (2014)

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Abstract. In this paper the authors evaluate in context of numerical calculations accuracy classical integer order and direct non-integer based order numerical algorithms of non-integer orders derivatives and integrals computations. Classical integer order based algorithm involves integer and fractional order differentiation and integration operators concatenation to obtain non-integer order. Riemann-Liouville and Caputo formulas are applied to obtain directly derivatives and integrals of non-integer orders. The following accuracy comparison analysis enables to answer the question, which algorithm of the two is burdened with lower computational error. The accuracy is estimated applying non-integer order derivatives and integrals computational formulas of some elementary functions available in the literature of the subject.