Fractional calculus and the ESR test

Abstract

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.

Keywords

• ESR| Mittag-Leffler functions| time-fractional PDE| Wright function