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Measurement of para-xylene diffusivity in zeolites and analyzing desorption curves using the Mittag-Leffler function

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Published/Copyright: May 5, 2016
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Fractional Calculus and Applied Analysis
From the journal Fractional Calculus and Applied Analysis Volume 19 Issue 2

Abstract

The new fractional calculus modeling based on Mittag-Leffler function has been employed to generate a better fit model to analyze the ZLC desorption curves for para-xylene diffusion in ZSM-5 zeolites. The diffusivity values generated herewith at 100, 125 and 150°C are reported as 4.4×10−13, 4.98 ×10−13 and 5.2 ×10−13m2/s, respectively. The activation energy for this diffusion process is found 4.2 kJ/mol and diffusion proportional constant (D0) is 1.85 × 10−12m2/s. The simplified model for ZLC response can be a better way to treat desorption data in ZLC experiments.

Key Words and Phrases: fractional calculus; Mittag-Leffler function; diffusion; para-xylene; Zeolite Socony Mobile (ZSM)-5; zero length column (ZLC) technique
MSC 2010: Primary 26A33; Secondary 33E12; 65R10; 93E12; 93A30

Acknowledgments

The authors gratefully acknowledge the research facilities provided by the Chemical and Materials Engineering Department at King Abdulaziz University, Jeddah, Saudi Arabia. The work of Ivo Petráš was supported in part by the Slovak Grant Agency for Science under Grants VEGA: 1/0552/14, 1/0908/15, and by the Slovak Research and Development Agency under the Contracts No. APVV-0482-11, No. SK-PL-2015-0038 and No. APVV-14-0892.

  1. Please cite to this paper as published in: Fract. Calc. Appl. Anal., Vol. 19, No 2 (2016), pp. 551–560, DOI: 10.1515/fca-2016-0028

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Received: 2015-9-30
Published Online: 2016-5-5
Published in Print: 2016-4-1

© 2016 Diogenes Co., Sofia

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA-Volume 19-2-2016)
  4. Survey Paper
  5. A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations
  6. Survey Paper
  7. A free fractional viscous oscillator as a forced standard damped vibration
  8. Research Paper
  9. On a Legendre Tau method for fractional boundary value problems with a Caputo derivative
  10. Research Paper
  11. Nonlinear Dirichlet problem with non local regional diffusion
  12. Research Paper
  13. Generalized fraction evolution equations with fractional Gross Laplacian
  14. Research Paper
  15. A stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equation
  16. Research Paper
  17. Convolutional approach to fractional calculus for distributions of several variables
  18. Research Paper
  19. Existence theorems for semi-linear Caputo fractional differential equations with nonlocal discrete and integral boundary conditions
  20. Research Paper
  21. Nonlinear Riemann-Liouville fractional differential equations with nonlocal Erdelyi-Kober fractional integral conditions
  22. Research Paper
  23. Spatial dispersion of elastic waves in a bar characterized by tempered nonlocal elasticity
  24. Research Paper
  25. Applications of the fractional Sturm-Liouville problem to the space-time fractional diffusion in a finite domain
  26. Short Paper
  27. Measurement of para-xylene diffusivity in zeolites and analyzing desorption curves using the Mittag-Leffler function
  28. Short Paper
  29. Monotonicity of functions and sign changes of their Caputo derivatives
  30. Short Note
  31. On the Volterra μ-functions and the M-Wright functions as kernels and eigenfunctions of Volterra type integral operators
https://doi.org/10.1515/fca-2016-0028
Keywords for this article
fractional calculus; Mittag-Leffler function; diffusion; para-xylene; Zeolite Socony Mobile (ZSM)-5; zero length column (ZLC) technique

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. FCAA related news, events and books (FCAA-Volume 19-2-2016)
  4. Survey Paper
  5. A survey of Lyapunov functions, stability and impulsive Caputo fractional differential equations
  6. Survey Paper
  7. A free fractional viscous oscillator as a forced standard damped vibration
  8. Research Paper
  9. On a Legendre Tau method for fractional boundary value problems with a Caputo derivative
  10. Research Paper
  11. Nonlinear Dirichlet problem with non local regional diffusion
  12. Research Paper
  13. Generalized fraction evolution equations with fractional Gross Laplacian
  14. Research Paper
  15. A stochastic solution with Gaussian stationary increments of the symmetric space-time fractional diffusion equation
  16. Research Paper
  17. Convolutional approach to fractional calculus for distributions of several variables
  18. Research Paper
  19. Existence theorems for semi-linear Caputo fractional differential equations with nonlocal discrete and integral boundary conditions
  20. Research Paper
  21. Nonlinear Riemann-Liouville fractional differential equations with nonlocal Erdelyi-Kober fractional integral conditions
  22. Research Paper
  23. Spatial dispersion of elastic waves in a bar characterized by tempered nonlocal elasticity
  24. Research Paper
  25. Applications of the fractional Sturm-Liouville problem to the space-time fractional diffusion in a finite domain
  26. Short Paper
  27. Measurement of para-xylene diffusivity in zeolites and analyzing desorption curves using the Mittag-Leffler function
  28. Short Paper
  29. Monotonicity of functions and sign changes of their Caputo derivatives
  30. Short Note
  31. On the Volterra μ-functions and the M-Wright functions as kernels and eigenfunctions of Volterra type integral operators
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