descriptionPublicationkeyboard_double_arrow_right Article 07 May 2021 English Publisher:Springer Science and Business Media LLCJournal:Meccanica, volume 57, pages 861-870 (issn: 0025-6455, eissn: 1572-9648,

Authors: Tomasz Blaszczyk; Krzysztof Bekus; Krzysztof Szajek; Wojciech Sumelka;

doi: 10.1007/s11012-021-01364-w

Approximation and application of the Riesz-Caputo fractional derivative of variable order with fixed memory

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Abstract

AbstractIn this paper, the Riesz-Caputo fractional derivative of variable order with fixed memory is considered. The studied non-integer differential operator is approximated by means of modified basic rules of numerical integration. The three proposed methods are based on polynomial interpolation: piecewise constant, piecewise linear, and piecewise quadratic interpolation. The errors generated by the described methods and the experimental rate of convergence are reported. Finally, an application of the Riesz-Caputo fractional derivative of space-dependent order in continuum mechanics is depicted.

Related Organizations

Poznań University of Technology
Poland
Częstochowa University of Technology
Poland

Keywords

fractional continuum model, Numerical and other methods in solid mechanics, Theory of constitutive functions in solid mechanics, polynomial interpolation, numerical integration, non-integer differential operator, Applications of fractional calculus in solid mechanics

2 Research products, page 1 of 1

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