Fractional calculus and the ESR test

J. Vanterler da C. Sousa; E. Capelas de Oliveira; L. A. Magna; J. Vanterler da C. Sousa; E. Capelas de Oliveira; L. A. Magna

doi:10.3934/Math.2017.4.692

AIMS Mathematics

2017, Volume 2, Issue 4: 692-705. doi: 10.3934/Math.2017.4.692

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Research article

Fractional calculus and the ESR test

1.
Department of Applied Mathematics, Imecc–Unicamp, Sérgio Buarque de Holanda, 651 13083–859, Campinas, SP, Brazil
2.
Department of Medical Genetics, School of Medical Sciences–Unicamp, 13083–887, Campinas, SP, Brazil

Received: 21 August 2017 Accepted: 08 December 2017 Published: 15 December 2017
MSC : 26A33, 33RXX, 34A30, 35KXX, 92BXX

We consider the partial differential equation of a mathematical model proposed by Sharma et al. ^[1] to describe the concentration of nutrients in blood, a factor which influences erythrocyte sedimentation rate. Introducing in it a fractional derivative in the Caputo sense, we create a new, timefractional mathematical model which contains, as a particular case, the original model. We obtain an analytic solution of this time-fractional partial differential equation in terms of Mittag-Leffler and Wright functions and to show that our model is more realistic than the Sharma model.
- ESR,
- Mittag-Leffler functions,
- time-fractional PDE,
- Wright function
Citation: J. Vanterler da C. Sousa, E. Capelas de Oliveira, L. A. Magna. Fractional calculus and the ESR test[J]. AIMS Mathematics, 2017, 2(4): 692-705. doi: 10.3934/Math.2017.4.692

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Abstract

We consider the partial differential equation of a mathematical model proposed by Sharma et al. ^[1] to describe the concentration of nutrients in blood, a factor which influences erythrocyte sedimentation rate. Introducing in it a fractional derivative in the Caputo sense, we create a new, timefractional mathematical model which contains, as a particular case, the original model. We obtain an analytic solution of this time-fractional partial differential equation in terms of Mittag-Leffler and Wright functions and to show that our model is more realistic than the Sharma model.

References

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