Fractional calculus and the ESR test

Abstract

We consider the partial differential equation of a mathematical model proposed by Sharma et al. ^{[<span class="xref"><a href="#b1" ref-type="bibr">1</a></span>]} 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.