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A multi-term fractional diffusion equation for oxygen delivery through a capillary to tissues. (English) Zbl 1190.35226
Summary: 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.
35R11Fractional partial differential equations
45J05Integro-ordinary differential equations
92C30Physiology (general)
65L99Numerical methods for ODE
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