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Mathematical Problems in Engineering
Volume 2013 (2013), Article ID 642101, 10 pages
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.
- M. C. dos Santos and E. Lenzi, “The use of aquatic macrophytes (Eichhornia crassipes) as a biological filter in the treatment of lead contaminated effluents,” Environmental Technology, vol. 21, no. 6, pp. 615–622, 2000.
- M. D. Machado, E. V. Soares, and H. M. V. M. Soares, “Selective recovery of chromium, copper, nickel, and zinc from an acid solution using an environmentally friendly process,” Environmental Science and Pollution Research, vol. 18, pp. 1279–1285, 2011.
- T. S. Mthombo, A. K. Mishra, S. B. Mishra, and B. B. Mamba, “The adsorption behavior of Cu(II), Pb(II), and Co(II) of ethylene vinyl acetate-clinoptilolite nanocomposites,” Journal of Applied Polymer Science, vol. 121, no. 6, pp. 3414–3424, 2011.
- J. G. Ibanez, P. Balderas-Hernandez, E. Garcia-Pintor et al., “Laboratory experiments on the electrochemical remediation of the environment—part 9: microscale recovery of a soil metal pollutant and its extractant,” Journal of Chemical Education, vol. 88, no. 8, pp. 1123–1125, 2011.
- E. Tel-Or and C. Forni, “Phytoremediation of hazardous toxic metals and organics by photosynthetic aquatic systems,” Plant Biosystems, vol. 145, no. 1, pp. 224–235, 2011.
- M. Asteasuain, M. Soares, M. K. Lenzi et al., “‘Living’ free radical polymerization in tubular reactors. I. Modeling of the complete molecular weight distribution using probability generating functions,” Macromolecular Reaction Engineering, vol. 1, no. 6, pp. 622–634, 2007.
- D. D. Do, Adsorption Analysis: Equilibria and Kinetics, Imperial College Press, London, UK, 1st edition, 1998.
- J. T. Machado, V. Kiryakova, and F. Mainardi, “Recent history of fractional calculus,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1140–1153, 2011.
- V. Z. Povstenko, “Fractional heat conduction equation and associated thermal stress,” Journal of Thermal Stresses, vol. 28, no. 1, pp. 83–102, 2005.
- I. S. Jesus and J. A. Tenreiro Machado, “Application of integer and fractional models in electrochemical systems,” Mathematical Problems in Engineering, vol. 2012, Article ID 248175, 17 pages, 2012.
- J. Klafter, S. C. Lim, and R. Metzler, Eds., Fractional Dynamics: Recent Advances, World Scientific Publishing Company, Singapore, 2011.
- K. Tas, J. A. T. Machado, and D. Baleanu, Eds., Mathematical Methods in Engineering,, Springer, Dordrecht, The Netherlands, 2007.
- J. Sabatier, O. P. Agrawal, and J. A. T. Machado, Eds., Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, Springer, Dordrecht, The Netherlands, 2007.
- D. Baleanu, J. A. T. Machado, and Z. B. Guvenc, Eds., New Trends in Nanotechnology and Fractional Calculus Applications, Springer, Dordrecht, The Netherlands, 2010.
- L. A. D. Isfer, M. K. Lenzi, and E. K. Lenzi, “Identification of biochemical reactors using fractional differential equations,” Latin American Applied Research, vol. 40, no. 2, pp. 193–198, 2010.
- J. Hristov, “A short-distance integral-balance solution to a strong subdiffusion equation: a weak power-law profile,” International Review of Chemical Engineering, vol. 2, pp. 555–563, 2010.
- J. Hristov, “Heat-balance integral to fractional (half-time) heat diffusion sub-model,” Thermal Science, vol. 14, no. 2, pp. 291–316, 2010.
- R. A. Pfaffenzeller, M. K. Lenzi, and E. K. Lenzi, “Modeling of granular material mixing using fractional calculus,” International Review of Chemical Engineering, vol. 3, pp. 818–821, 2011.
- R. L. Magin, “Fractional calculus models of complex dynamics in biological tissues,” Computers & Mathematics with Applications, vol. 59, pp. 1586–1593, 2010.
- M. Khan, S. H. Ali, C. Fetecau, and H. Qi, “Decay of potential vortex for a viscoelastic fluid with fractional Maxwell model,” Applied Mathematical Modelling, vol. 33, no. 5, pp. 2526–2533, 2009.
- R. F. Camargo, E. C. de Oliveira, and J. Vaz Jr., “On the generalized Mittag-Leffler function and its application in a fractional telegraph equation,” Mathematical Physics, Analysis and Geometry, vol. 15, pp. 1–16, 2012.
- M. C. dos Santos, E. Lenzi, E. M. Gomes, M. K. Lenzi, and E. K. Lenzi, “Development of heavy metal sorption isotherm using fractional calculus,” International Review of Chemical Engineering, vol. 3, pp. 814–817, 2011.
- A. L. Alberton, M. Schwaab, M. Schmal, and J. C. Pinto, “Experimental errors in kinetic tests and its influence on the precision of estimated parameters—part I: analysis of first-order reactions,” Chemical Engineering Journal, vol. 155, pp. 816–823, 2009.
- M. Joshi, A. Kremling, and A. Seidel-Morgenstern, “Model based statistical analysis of adsorption equilibrium data,” Chemical Engineering Science, vol. 61, no. 23, pp. 7805–7818, 2006.
- J. D. Gabano and T. Poinot, “Fractional modelling and identification of thermal systems,” Signal Processing, vol. 91, no. 3, pp. 531–541, 2011.
- F. Khemane, R. Maltia, T. Raïssic, and X. Moreaua, “Robust estimation of fractional models in the frequency domain using set membership methods,” Signal Processing, vol. 92, pp. 1591–1601, 2012.
- A. Almusharff and N. Nguyen, “A combination of time-scale calculus and a cross-validation technique used in fitting and evaluating fractional models,” Applied Mathematics Letters, vol. 25, no. 3, pp. 550–554, 2012.
- G. E. P. Box and W. G. Hunter, “A useful method for model-building,” Technometrics, vol. 4, pp. 301–318, 1962.
- G. E. P. Box and P. W. Tidwell, “Transformation of the independent variables,” Technometrics, vol. 4, pp. 531–550, 1962.
- I. Podlubny, Fractional Differential Equations, Academic Press, New York, NY, USA, 1st edition, 1999.
- P. Englezos and N. Kalogerakis, Applied Parameter Estimation for Chemical Engineers, Marcel Dekker, New York, NY, USA, 1st edition, 2001.
- Y. Bard, Nonlinear Parameter Estimation, Academic Press, New York, NY, USA, 1st edition, 1974.
- D. M. Himmelblau, Process Analysis by Statistical Methods, John Wiley & Sons, New York, NY, USA, 1st edition, 1970.
- I. Guttman and D. A. Meeter, “On Beale's measures of non-linearity,” Technometrics, vol. 7, pp. 623–637, 1965.
- J. C. Pinto and M. Schwaab, Análise de Dados Experimentais. I. Fundamentos de Estatística e Estimação de Parâmetros, Editora e-Papers, Rio de Janeiro, Brazil, 1st edition, 2007.
- M. Giona and H. E. Roman, “A theory of transport phenomena in disordered systems,” The Chemical Engineering Journal, vol. 49, no. 1, pp. 1–10, 1992.
- E. K. Lenzi, H. V. Ribeiro, J. Martins, M. K. Lenzi, G. G. Lenzi, and S. Specchia, “Non-Markovian diffusion equation and diffusion in a porous catalyst,” Chemical Engineering Journal, vol. 172, pp. 1083–1087, 2011.
- N. N. Lebedev, Special Functions and Their Applications, Dover Publications, New York, NY, USA, 1st edition, 1972.