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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.
MSC:
35R11Fractional partial differential equations
45J05Integro-ordinary differential equations
92C30Physiology (general)
65L99Numerical methods for ODE
References:
[1]Leach, R. M.; Treacher, D. F.: ABC of oxygen. Oxygen transport-2. Tissue hypoxia, Clinical rev. BMJ 317, 1370-1373 (1998)
[2]Wang, C. Y.; Bassingthwaighte, J. B.: Capillary supply regions, Math. biosci. 173, No. 2, 103 (2001) · Zbl 0984.92011 · doi:10.1016/S0025-5564(01)00074-8
[3]Go, Jaegwi: Oxygen delivery through capillaries, Math. biosci. 208, 166-176 (2007) · Zbl 1116.92021 · doi:10.1016/j.mbs.2006.09.021
[4]Wazwaz, A. M.: A reliable modification of Adomian decomposition method, Appl. math. Comput. 102, 77-86 (1999) · Zbl 0928.65083 · doi:10.1016/S0096-3003(98)10024-3
[5]Daftardar-Gejji, V.; Jafari, H.: An iterative method for solving nonlinear functional equations, J. math. Anal. appl. 316, 753-763 (2006) · Zbl 1087.65055 · doi:10.1016/j.jmaa.2005.05.009
[6]Daftardar-Gejji, V.; Bhalekar, S.: Solving fractional diffusion-wave equations using a new iterative method, Frac. calc. Appl. anal. 11, No. 2, 193-202 (2008) · Zbl 1210.26009
[7]Bhalekar, S.; Daftardar-Gejji, V.: New iterative method: application to partial differential equations, Appl. math. Comput. 203, 778-783 (2008) · Zbl 1154.65363 · doi:10.1016/j.amc.2008.05.071
[8]Adomian, G.: A review of the decomposition method in applied mathematics, J. math. Anal. appl. 135, 501-544 (1988) · Zbl 0671.34053 · doi:10.1016/0022-247X(88)90170-9
[9]Adomian, G.: Solving frontier problems of physics: the decomposition method, (1994)
[10]Adomian, G.: Solutions of nonlinear PDE, Appl. math. Lett. 11, 121-123 (1998) · Zbl 0933.65121 · doi:10.1016/S0893-9659(98)00043-3
[11]Adomian, G.; Rach, R.: Linear and nonlinear Schrödinger equations, Found phys. 21, 983-991 (1991)
[12]Wazwaz, A. M.: Partial differential equations: methods and applications, (2002)
[13]Wazwaz, A. M.: The decomposition method applied to systems to PDE and to the reaction–diffusion Brusselator model, Appl. math. Comput. 110, 251-264 (2000)
[14]Wazwaz, A. M.: Approximate solutions to boundary value problems of higher order by the modified decomposition method, Comput. math. Appl. 40, 679-691 (2000) · Zbl 0959.65090 · doi:10.1016/S0898-1221(00)00187-5
[15]Wazwaz, A. M.: The modified decomposition method applied to unsteady flow of gas through a porous medium, Appl. math. Comput. 118, 123-132 (2001) · Zbl 1024.76056 · doi:10.1016/S0096-3003(99)00209-X
[16]Kaya, D.; Yokus, A.: A numerical comparison of partial solutions in the decomposition method for linear and nonlinear partial differential equation, Math. comput. Simul. 60, 507-512 (2002) · Zbl 1007.65078 · doi:10.1016/S0378-4754(01)00438-4
[17]Ray, S. Saha: A numerical solution of the coupled sine–Gordon equation using the modified decomposition method, Appl. math. Comput. 175, 1046-1054 (2006) · Zbl 1093.65098 · doi:10.1016/j.amc.2005.08.018
[18]Daftardar-Gejji, V.; Bhalekar, S.: Solving multi-term linear and non-linear diffusion–wave equations of fractional order by Adomian decomposition method, Appl. math. Comput. 202, 113-120 (2008) · Zbl 1147.65106 · doi:10.1016/j.amc.2008.01.027
[19]Manolis, G. D.; Rangelov, T. V.: Non-homogeneous elastic waves in soils: notes on the vector decomposition technique, Soil dyn. Earthq. eng. 26, 952-959 (2006)
[20]Luchko, Yu.; Gorenflo, R.: An operational method for solving fractional differential equations with the Caputo derivatives, Acta math. Vietnam 24, 207-233 (1999) · Zbl 0931.44003