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Fractional Calculus and Applied Analysis

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Volume 18, Issue 4


Fractional Pennes’ Bioheat Equation: Theoretical and Numerical Studies

Luis L. Ferrás
  • Institute for Polymers and Composites/I3N University of Minho Campus de Azurém 4800-058 Guimares, PORTUGAL
  • Department of Mathematics University of Chester, CH1 4BJ, UK
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/ Neville J. Ford / Maria L. Morgado / João M. Nóbrega / Magda S. Rebelo
  • Departamento de Matemática and Centro de Matemática e Aplicącões Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa Quinta da Torre, 2829-516 Caparica, PORTUGAL
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Published Online: 2015-08-04 | DOI: https://doi.org/10.1515/fca-2015-0062


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.

Keywords : fractional differential equations; Caputo derivative; bioheat equation; stability; convergence


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About the article

Received: 2015-02-13

Published Online: 2015-08-04

Published in Print: 2015-08-01

Citation Information: Fractional Calculus and Applied Analysis, Volume 18, Issue 4, Pages 1080–1106, ISSN (Online) 1314-2224, ISSN (Print) 1311-0454, DOI: https://doi.org/10.1515/fca-2015-0062.

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