Application of integer and fractional models in electrochemical systems

Mathematical Problems in Engineering

Volumn 2012, Issue , 2012, Pages

  Jesus, Isabel S ^a   Tenreiro MacHado, J A ^a  

^a INSTITUTO SUPERIOR DE ENGENHARIA DO PORTO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

ELECTRICAL COMPONENTS; ELECTRICAL ELEMENTS; ELECTROCHEMICAL SYSTEMS; FRACTAL ELECTRODES; FRACTIONAL MODEL; FREQUENCY DOMAINS;

ENGINEERING; MATHEMATICAL TECHNIQUES;

FREQUENCY DOMAIN ANALYSIS;

EID: 84856397621     PISSN: 1024123X     EISSN: 15635147     Source Type: Journal    
DOI: 10.1155/2012/248175     Document Type: Article

References (32)

1. Oldham K. B., Spanier J., The Fractional Calculus 1974 11 London, UK Academic Press xiii+234 Mathematics in Science and Engineering
2. Oldham K. B., Spanier J., Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order 1974 London, UK Academic Press xiii+234
3. Samko S. G., Kilbas A. A., Marichev O. I., Fractional Integrals and Derivatives: Theory and Applications 1993 Yverdon, Switzerland Gordon and Breach Science Publishers xxxvi+976
4. Miller K. S., Ross B., An Introduction to the Fractional Calculus and Fractional Differential Equations 1993 New York, NY, USA John Wiley Sons xvi+366
5. Kilbas A. A., Srivastava H. M., Trujillo J. J., Theory and Applications of Fractional Differential Equations 2006 204 Amsterdam, The Netherlands Elsevier Science B.V. xvi+523 North-Holland Mathematics Studies
6. Monda D., Biswas K., Electrical equivalent modeling of single component fractional order element with porous surface Proceedings of the 5th International Conference on Sensor Technologies and Applications (SENSORCOMM '11) August 2011 312 316
7. Mondal D., Biswas K., Performance study of fractional order integrator using single-component fractional order element IET Circuits, Devices Systems 2011 5 4 334 342
8. Biswas K., Studies on design, development and performance analysis of capacitive type sensors, Ph.D. thesis 2007 Kharagpur, India Indian Institute of Technology
9. Carpinteri A., Mainardi F., Fractals and Fractional Calculus in Continuum Mechanics 1997 378 Vienna, Austria Springer vi+348 CISM Courses and Lectures
10. Debnath L., Fractional Calculus and Its Applications 2002
11. Machado J. A. T., Jesus I. S., A suggestion from the past? FCAAJournal of Fractional Calculus Applied Analysis 2005 7 4 403 407
12. Jesus I. S., Machado J. A. T., Cunha J. B., Silva M. F., Fractional order electrical impedance of fruits and vegetables Proceedings of the 25th IASTED International Conference on Modelling, Identification, and Control (MIC '06) January 2006 489 494
13. Magin R. L., Fractional Calculus in Bioengineering 2006 Paris, France Begell House Connecticut
14. Baleanu D., Golmankhaneh A. K., Nigmatullin R. R., Newtonian law with memory Nonlinear Dynamics 2010 60 1-2 81 86
15. Bhalekar S., Daftardar-Gejji V., Baleanu D., Magin R., Fractional Bloch equation with delay Computers Mathematics with Applications 2011 61 5 1355 1365
16. Ionescu C. M., Keyser R. D., Relations between fractional-order model parameters and lung pathology in chronic obstructive pulmonary disease IEEE Transactions on Biomedical Engineering 2009 56 4 978 987
17. Hedrih K. R. S., Energy transfer in the hybrid system dynamics (energy transfer in the axially moving double belt system) Archive of Applied Mechanics 2009 79 6-7 529 540
18. Samavati H., Hajimiri A., Shahani A. R., Nasserbakht G. N., Lee T. H., Fractal capacitors IEEE Journal of Solid-State Circuits 1998 33 12 2035 2041 (Pubitemid 128568603)
19. Jonscher A. K., Dielectric Relaxation in Solids 1993 London, UK Chelesea Dielectric Press
20. Bohannan G. W., Analog Realization of a Fractional Order Control Element 2002 Bozeman, Mo, USA Wavelength Electronics
21. Bohannan G. W., Interpretation of Complex Permittivity in Pure and Mixed Crystals Wavelength Electronics
22. Westerlund S., Ekstam L., Capacitor theory IEEE Transactions on Dielectrics and Electrical Insulation 1994 1 5 826 839
23. Westerlund S., Dead Matter has Memory! 2002 Kalmar, Sweden Causal Consulting
24. Barsoukov E., Macdonald J. R., Impedance Spectroscopy, Theory, Experiment, and Applications 2005 John Wiley Sons
25. Jesus I. S., Machado J. A. T., Cunha J. B., Fractional electrical dynamics in fruits and vegetables Proceedings of the 2nd IFAC Workshop on Fractional Differentiation and its Applications (FDA '06) 2006 374 379
26. Jesus I. S., Tenreiro MacHado J. A., Boaventure Cunha J., Fractional electrical impedances in botanical elements Journal of Vibration and Control 2008 14 9-10 1389 1402
27. Jesus I. S., MacHado J. A. T., Development of fractional order capacitors based on electrolyte processes Nonlinear Dynamics 2009 56 1-2 45 55
28. Jesus I. S., Machado J. A. T., Silva M. F., Fractional order capacitors Proceedings of the 27th IASTED International Conference on Modelling, Identification, and Control (MIC '08) February 2008
29. Jesus I. S., Machado J. A. T., Barbosa R. S., Fractional modelling of the electrical conduction in nacl electrolyte Proceedings of the 6th EUROMECH Conference (ENOC '08) June 2008 Saint Petersburg, RUSSIA
30. Le Méhauté A., Nigmatullin R. R., Nivanen L., Flches du Temps et Géométrie Fractale 1998 2nd Paris, France Herms 350
31. Falconer K., Fractal GeometryMathematical Foundations and Application 1990 England, UK John Wiley Sons xxii+288
32. Jesus I. S., Machado J. A. T., Comparing integer and fractional models in some electrical systems Proceedings of the 4th IFAC Workshop on Fractional Differentiation and its Applications (FDA '10) October 2010 Badajoz, Spain