AIMS Mathematics, 2017, 2(4): 692-705. doi: 10.3934/Math.2017.4.692.

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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

We consider the partial differential equation of a mathematical model proposed by Sharmaet al. [1] to describe the concentration of nutrients in blood, a factor which influences erythrocytesedimentation rate. Introducing in it a fractional derivative in the Caputo sense, we create a new, timefractionalmathematical model which contains, as a particular case, the original model. We obtainan analytic solution of this time-fractional partial differential equation in terms of Mittag-Leffler andWright functions and to show that our model is more realistic than the Sharma model.
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Keywords 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. AIMS Mathematics, 2017, 2(4): 692-705. doi: 10.3934/Math.2017.4.692


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