Solution of inverse anomalous mass transfer problems using a hyperbolic space-fractional model and differential evolution


  • Felipe Augusto Paes de Godoi
  • Fran Sérgio Lobato
  • João Jorge Ribeiro Damasceno



fick law, inverse anomalous problem, real experimental data, fractional hyperbolic advection-dispersion model, differential evolution


The study of anomalous diffusion phenomenon characterizes an important field of science due to limitations of traditional laws considered to represent the conduction term found in mass and heat transfer models. Mathematically, this phenomenon can be represented by empirical and phenomenological models with different levels of complexity. For the latter, differential models with fractional order have been considered. In addition, based on hyperbolic diffusion theory, this fractional differential model can be represented by a second-order derivative on time. This fractional hyperbolic differential model presents two new parameters (fractional order and time relaxation factor) that should be estimated. For this purpose, an inverse problem considering experimental data needs to be formulated and solved. In this context, the present contribution aims to formulate and solve two inverse anomalous diffusion problems considering a fractional hyperbolic advection-dispersion model to obtain the fractional order and the time relaxation tensor using real experimental data sets. To solve the direct problem the Finite Difference Method is extended for fractional context by using Grünwald-Letnikov Derivative. To solve each inverse problem, the Differential Evolution algorithm is considered as an optimization tool. The obtained results are compared with those found considering the simplification of the hyperbolic space-fractional model. In all analyzed cases, the DE algorithm was able to find good estimates for both parameters and it was demonstrated that the objective function considering the fractional hyperbolic advection-dispersion resulted in lower residual values.


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How to Cite

de Godoi, F. A. P., Lobato, F. S., & Damasceno, J. J. R. (2023). Solution of inverse anomalous mass transfer problems using a hyperbolic space-fractional model and differential evolution. OBSERVATÓRIO DE LA ECONOMÍA LATINOAMERICANA, 21(12), 26050–26075.




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