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Determining the Time Elapsed Since Sudden Localized Impulse Given to Fractional Advection Diffusion Equation

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Theory and Applications of Non-integer Order Systems

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 407))

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Abstract

In some natural media solute transport is ruled by a fractional Advection Diffusion Equation that accounts for fluid and chemicals stored in quiescent zones before being released after random times. An adjoint equation helps us deducing from concentration records where and at what time a solute has been suddenly injected in such media.

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References

  1. Schumer, R., Benson, D.A., Meerschaert, M.M., Baeumer, B.: Fractal mobile/immobile solute transport. Water Resour. Res. 39(10), 1296 (2003)

    Google Scholar 

  2. Benson, D.A., Meerschaert, M.M.: A simple and efficient random walk solution of multi-rate mobile/immobile mass transport equations. Adv. Water Resour. 32(4), 532–539 (2009)

    Article  Google Scholar 

  3. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, New York (1993)

    MATH  Google Scholar 

  4. Gorenflo, R., Luchko, Y., Yamamoto, M.: Time-fractional diffusion equation in the fractional Sobolev spaces. Fract. Calc. Appl. Anal. 18(3), 799–820 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Brezis, H.: Analyse Fonctionnelle, théorie et Applications. Masson, Paris (1983)

    Google Scholar 

  6. Levitan, B.M., Sargsjan, I.S.: Introduction to Spectral Theory: Selfadjoint Ordinary Differential Operators. Translations of Mathematical Monographs, vol. 39. American Mathematical Society, Providence (1975)

    MATH  Google Scholar 

  7. Luchko, Y.: Maximum principle for the generalized time-fractional differential diffusion equation. Acta. Math. Vietnam. 24(2), 141–160 (1999)

    MathSciNet  Google Scholar 

  8. Luchko, Y., Gorenflo, R.: An operational method for solving fractional differential equations with the Caputo derivatives. J. Math. Anal. Appl. 351, 218–223 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  9. Arendt, W., Batty, C.J.K., Hieber, M., Neubrander, F.: Vector-Valued Laplace Transforms and Cauchy Problems. Birkhäuser, Basel (2001)

    Book  MATH  Google Scholar 

  10. Baeumer, B., Meerschaert, M.M.: Stochastic solutions for fractional Cauchy problems. Fract. Calc. Appl. Anal. 4(4), 481–500 (2001)

    MathSciNet  MATH  Google Scholar 

  11. Diethelm, K., Ford, N.J., Freed, A.D., Luchko, Y.: Algorithms for the fractional calculus: a selection of numerical methods. Comput. Methods Appl. Mech. Eng. 194(6), 743–773 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pazy, A.: Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences, vol. 44. Springer, New York (1983)

    MATH  Google Scholar 

  13. Jacob, N.: Pseudo Differential Operators and Markov Processes. Imperial College Press, London (2001)

    Book  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. University of Avignon, Avignon, France

    Marie-Christine Néel

Authors
  1. Marie-Christine Néel
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Correspondence to Marie-Christine Néel .

Editor information

Editors and Affiliations

  1. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Artur Babiarz

  2. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Adam Czornik

  3. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Jerzy Klamka

  4. Institute of Automatic Control, Silesian University of Technology Institute of Automatic Control, Gliwice, Poland

    Michał Niezabitowski

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Néel, MC. (2017). Determining the Time Elapsed Since Sudden Localized Impulse Given to Fractional Advection Diffusion Equation. In: Babiarz, A., Czornik, A., Klamka, J., Niezabitowski, M. (eds) Theory and Applications of Non-integer Order Systems. Lecture Notes in Electrical Engineering, vol 407. Springer, Cham. https://doi.org/10.1007/978-3-319-45474-0_22

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  • DOI: https://doi.org/10.1007/978-3-319-45474-0_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-45473-3

  • Online ISBN: 978-3-319-45474-0

  • eBook Packages: EngineeringEngineering (R0)

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