A Non-Integer Order Blood Rheological Model in a Magneto-thermal Environment

Azhar Ali Zafar\(^{a,*}\), Maria Batool\(^a\), Muhammad Shahzaib\(^a\)

\(^a\)Department of Mathematics, Government College University, Lahore Pakistan.

Correspondence should be addressed to: azharalizafar@gcu.edu.pk,shamaria257@gmail.com,m.shahzaib@gcu.edu.pk

Copyright © 2025 Azhar Ali Zafar, Maria Batool, Muhammad Shahzaib. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: Received: 29 December 2024; Accepted: 01 May 2025; Published Online: 02 May 2025

Abstract

This study develops a rheological model for blood flow in an arterial segment using a non-integer order derivative modelling in the sense of Atangana-Baleanu fractional derivative operator. This model takes into consideration the effects of external magnetic flux, periodic body acceleration, and radiant heat on the behaviour of the blood. Integral transforms are employed to solve the problem. Expressions for temperature, concentration, and flow velocity of blood will be developed. Additionally, the effects of the fractional order parameter and other important factors on blood dynamics are examined by the aid of analytical and graphical analysis and key findings are concluded that helps to control blood rheology.

Keywords:

Coincidence point, MHD,, Integral transforms,, Blood flow,, Fractional order derivative operator.