A multi-term fractional diffusion equation for oxygen delivery through a capillary to tissues

Authors:
V. Srivastava;K. N. Rai
Affiliations:
DST-CIMS, Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi-221005, India;DST-CIMS, Department of Applied Mathematics, Institute of Technology, Banaras Hindu University, Varanasi-221005, India
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2010

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Abstract

In this article, we propose a new mathematical model, namely a multi-term fractional diffusion equation, for oxygen delivery through a capillary to tissues. Fractional calculus is applied to describe the phenomenon of subdiffusion of oxygen in both transverse and longitudinal directions. A new iterative method (NIM) and a modified Adomian decomposition method (MDM) are used to solve the multi-term fractional diffusion equation for different conditions. The results thus obtained are compared and presented graphically. It is observed that the order of the diffusion equation affects the delivery of oxygen significantly.