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Linear discrete systems with memory: a generalization of the Langmuir model

  • Research Article
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Central European Journal of Physics

Abstract

In this manuscript we analyzed a general solution of the linear nonlocal Langmuir model within time scale calculus. Several generalizations of the Langmuir model are presented together with their exact corresponding solutions.

The physical meaning of the proposed models are investigated and their corresponding geometries are reported.

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References

  1. I. Langmuir, J. Am. Chem. Soc. 38, 2221 (1916)

    Article  Google Scholar 

  2. J. Kankare, I. A. Vinokurov, Langmuir 15, 5591 (1999)

    Article  Google Scholar 

  3. A. Kapoor, J. A. Ritter, R. T. Yang, Langmuir 6, 660 (1990)

    Article  Google Scholar 

  4. G. Sauerbrey, Zeitsch. Phys. 155, 206 (1959)

    Article  ADS  Google Scholar 

  5. D. S. G. Karpovich, J. Blanchard, Langmuir 10, 3315 (1994)

    Article  Google Scholar 

  6. S. J. Gregg, K. S. W. Sing, Adsorption, Surface Area and Porosity (Academic Press, 1967)

    Google Scholar 

  7. Y. L. Sun et al., Talanta 73, 857 (2007)

    Article  Google Scholar 

  8. P. G. Su, Y. P. Chang, Sens. Actuators B 125, 915 (2008)

    Article  Google Scholar 

  9. M.C. Baleanu, R. R. Nigmatullin, S. Okur, K. Ocakoglu, Commun. Nonlinear Sci. 16, 4643 (2011)

    Article  MATH  Google Scholar 

  10. A. Erol, S. Okur, B. Comba, O. Mermer, M. C. Arikan, Sens. Actuators B 145, 174 (2010)

    Article  Google Scholar 

  11. A. A. Kilbas, H. H. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations (Elsevier, Amsterdam 2006)

    MATH  Google Scholar 

  12. S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives — Theory and Applications (Gordon and Breach, Linghorne, P.A. 1993)

    MATH  Google Scholar 

  13. R. L. Magin, Fractional Calculus in Bioengineering (Begell House Publisher, Inc. Connecticut 2006)

    Google Scholar 

  14. B. J. West, M. Bologna, P. Grigolini, Physics of Fractal operators (Springer, New York 2003)

    Book  Google Scholar 

  15. D. Baleanu, K. Diethelm, E. Scalas, J. J. Trujillo, Fractional Calculus Models and Numerical Methods (Series on Complexity, Nonlinearity and Chaos, World Scientific 2012)

    MATH  Google Scholar 

  16. J. A. T. Machado, V. Kiryakova, F. Mainardi, Commun. Nonlinear Sci. 16, 1140 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  17. M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications (Birkhäuser, Boston, Mass, USA, 2001)

    Book  Google Scholar 

  18. I. Podlubny, Fractional Differential Equations (Academic Press, San Diego CA 1999)

    MATH  Google Scholar 

  19. R. Bellman, Introduction to Matrix Analysis (Philadelphia: Society for Industrial and Applied Mathematics, 1997)

    Book  MATH  Google Scholar 

  20. R. R. Nigmatullin, D. Baleanu, Int. J. Theor. Phys. 49, 701 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  21. S. Hilger, Results in Mathematics 18, 18 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  22. G. Sh. Guseinov, J. Math. Anal. Appl. 285, 107 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics & Computer Science, Çankaya University, Ögretmenler Cad. 14, 06530, Balgat — Ankara, Turkey

    Dumitru Băleanu

  2. Institute of Space Sciences, Magurele-Bucharest, Romania

    Dumitru Băleanu

  3. Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box: 80204, Jeddah, 21589, Saudi Arabia

    Dumitru Băleanu

  4. Institute of Physics, Department of Theoretical Physics, Kazan (Volga region) Federal University, Kremlevskaia str. 18, 420008, Kazan, Tatarstan, Russia

    Raoul R. Nigmatullin

Authors
  1. Dumitru Băleanu
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  2. Raoul R. Nigmatullin
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Correspondence to Dumitru Băleanu.

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Băleanu, D., Nigmatullin, R.R. Linear discrete systems with memory: a generalization of the Langmuir model. centr.eur.j.phys. 11, 1233–1237 (2013). https://doi.org/10.2478/s11534-012-0129-5

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  • DOI: https://doi.org/10.2478/s11534-012-0129-5

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