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A real regularised fractional derivative

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Abstract

A real regularised integral formulation of the fractional derivative is obtained from the generalised Grünwald–Letnikov derivative without using the Cauchy derivative. This new approach is based on the properties of the Mellin transform. The usual Riemann–Liouville and Caputo derivatives are expressed in a similar way emphasising their regularising capabilities. Some examples involving the Heaviside unit step function are presented in the last section of the paper.

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Authors and Affiliations

  1. UNINOVA and Department of Electrical Engineering, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Campus da FCT da UNL, Quinta da Torre, 2829-516, Monte da Caparica, Portugal

    Manuel D. Ortigueira

  2. Bioengineering Department, University of Illinois at Chicago, 851 South Morgan, Room 212, Chicago, IL, 60607-7052, USA

    Richard L. Magin

  3. Departamento de Análisis Matemático, University of La Laguna, 38271, La Laguna, Tenerife, Spain

    Juan J. Trujillo

  4. Departamento de Matemática Aplicada, Facultad de Matemáticas, Universidad Complutense de Madrid, 28040, Madrid, Spain

    M. Pilar Velasco

Authors
  1. Manuel D. Ortigueira
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  2. Richard L. Magin
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  3. Juan J. Trujillo
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  4. M. Pilar Velasco
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Corresponding author

Correspondence to Manuel D. Ortigueira.

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Ortigueira, M.D., Magin, R.L., Trujillo, J.J. et al. A real regularised fractional derivative. SIViP 6, 351–358 (2012). https://doi.org/10.1007/s11760-012-0320-6

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  • DOI: https://doi.org/10.1007/s11760-012-0320-6

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