期刊
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
卷 18, 期 4, 页码 1080-1106出版社
WALTER DE GRUYTER GMBH
DOI: 10.1515/fca-2015-0062
关键词
fractional differential equations; Caputo derivative; bioheat equation; stability; convergence
资金
- FEDER through the COMPETE Programme
- FCT Portuguese Foundation for Science and Technology [UID/CTM/50025/2013, EXPL/CTM-POL/1299/2013]
- Portuguese Foundation for Science and Technology [SFRH/BPD/100353/2014, UID/MAT/00297/2013]
- Fundação para a Ciência e a Tecnologia [EXPL/CTM-POL/1299/2013] Funding Source: FCT
In this work we provide a new mathematical model for the Pennes' bioheat equation, assuming a fractional time derivative of single order. Alternative versions of the bioheat equation are studied and discussed, to take into account the temperature-dependent variability in the tissue perfusion, and both finite and infinite speed of heat propagation. The proposed bioheat model is solved numerically using an implicit finite difference scheme that we prove to be convergent and stable. The numerical method proposed can be applied to general reaction diffusion equations, with a variable diffusion coefficient. The results obtained with the single order fractional model, are compared with the original models that use classical derivatives.
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