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Mathematical Problems in Engineering
Volume 2013, Article ID 642101, 10 pages
Research Article

Parametric Analysis of a Heavy Metal Sorption Isotherm Based on Fractional Calculus

1Departamento de Engenharia Química, Universidade Federal do Paraná, Caixa Postal 19011, 81531-980 Curitiba, PR, Brazil
2Departamento de Física, Universidade Estadual de Maringá, 87020-900 Maringá, PR, Brazil

Received 5 October 2012; Revised 5 April 2013; Accepted 14 April 2013

Academic Editor: Jocelyn Sabatier

Copyright © 2013 Enrico M. Gomes et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Heavy metals are widely recognized as being hazardous to human health and environmentally aggressive. The literature reports different approaches for lead removal, for example, water hyacinths. Heavy metal sorption isotherm modeling represents an important tool towards the study of equilibrium conditions. Fractional calculus represents a novel approach and a growing research field for process modeling, based on derivatives of arbitrary order. Recently, a novel isotherm based on fractional calculus was proposed for lead sorption using water hyacinth (Eichhornia crassipes). This paper reports a general procedure on error analysis and its influence on parameter estimation. It was applied to mathematical models based on fractional differential equations, focusing on a heavy metal novel isotherm sorption model. Parameter variance was calculated by using two different approaches (with the complete Hessian matrix and with a simplified Hessian matrix), and joint parameter confidence regions were generated, being successfully able to show that the fractional nature of the model is statistically valid.