Incorporation of concentration gradient of blood nutrients in Erythrocyte Sedimentation Rate fractional model with non‐zero uniform average blood velocity

Abstract

A new insight is presented into the solution of the erythrocyte sedimentation rate (ESR) model, based on fractional derivative with respect to time, with non‐zero uniform velocity of blood by incorporating the concentration gradient of the blood nutrients. An analytical solution is acquired for the modified ESR fractional model in addition to presenting some new interesting results. The best possible suitable range for the concentration gradient is found for the model whose use will be helpful in approximating the clinical data from laboratory tests in a profound and accurate manner and also in diagnosing the ESR rate more accurately. Further, an appropriate range is proposed for the uniform velocity of blood as well as the fractional order of the time derivative to construct the feasible model. In addition, it is also shown what value of the fractional order gives a closer resemblance to the clinical data. Validation and verification of the obtained results against earlier results demonstrate the effectiveness of the proposed model.