Fractional pennes' bioheat equation: theoretical and numerical studies

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.

Fractional bioheat equation

In this work we develop a new mathematical model for the Pennes’ bioheat equation assuming a fractional time derivative of single order. A numerical method for the solu- tion of such equations is proposed, and, the suitability of the new model for modelling real physical problems is studied and discussed

Comparison of different numerical methods for the solution of the time-fractional reaction-diffusion equation with variable diffusion coefficient

In this work we perform a comparison of two different numerical schemes for the solution of the time-fractional diffusion equation with variable diffusion coefficient and a nonlinear source term. The two methods are the implicit numerical scheme presented in [M.L. Morgado, M. Rebelo, Numerical approximation of distributed order reaction- diffusion equations, Journal of Computational and Applied Mathematics 275 (2015) 216-227] that is adapted to our type of equation, and a colocation method where Chebyshev polynomials are used to reduce the fractional differential equation to a system of ordinary differential equations

Social entrepreneurship: does institutional environment make a difference?

The purpose of this paper is to contribute to a better understanding of the link between social entrepreneurs and institutional environment in Portugal. A quantitative approach is used in the study, and primary data were collected through an online survey. A questionnaire was emailed to, both, Portuguese Non-Governmental organizations and projects available on the Portuguese social stock exchange. In the analysis of the data were used descriptive statistics, factorial analysis and t-student tests to validate (or not) the research hypotheses. The results show that a favorable institutional environment has a low importance in the decision to develop social initiatives. This conclusion supports the idea that many social entrepreneurs can emerge even in developing regions where the institutional environment is weak. Therefore, social entrepreneurship could be an instrument of regional development and contribute to attenuate the social and economic differences among Portuguese regions.