### AIMS Mathematics

2017, Issue 4: 692-705. doi: 10.3934/Math.2017.4.692
Research article

# Fractional calculus and the ESR test

• 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.

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

### Related Papers:

• 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.

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