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Waves in Random and Complex Media Volume 34, 2024 - Issue 3
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Research Articles

Formulation of space-angular fractional radiative transfer equation in participating finite slab clumpy media

M. Sallaha Astrophysics and Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt;b Higher Institute for Engineering and Technology, New Damietta, EgyptCorrespondence[email protected]
,
R. Gamala Astrophysics and Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt
,
A. Elgarayhia Astrophysics and Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt
&
A. A. Mahmouda Astrophysics and Theoretical Physics Research Group, Physics Department, Faculty of Science, Mansoura University, Mansoura, Egypt
Pages 1407-1418 | Received 17 Jan 2021, Accepted 31 May 2021, Published online: 10 Jun 2021

References

  • Cattaneo C. Sulla conduzione del calore. Atti Sem Mat Fis Univ Modena. 1948;3:83–101.
  • Klages R, Radons G, Sokolov IM. eds. Anomalous transport: foundations and applications. Weinheim: John Wiley & Sons; 2008.
  • Vyawahare VA, Nataraj PSV. Fractional-order modeling of neutron transport in a nuclear reactor. Appl Math Model. 2013;37(23):9747–9767.
  • Bovet A, Gamarino M, Furno I, et al. Transport equation describing fractional lévy motion of suprathermal ions in TORPEX. Nucl Fusion. 2014;54(10):104009.
  • Philippa B, Robson RE, White RD. Generalized phase-space kinetic and diffusion equations for classical and dispersive transport. New J Phys. 2014;16(7):073040.
  • Metzler R, Klafter J. The random walk’s guide to anomalous diffusion: a fractional dynamics approach. Phys Rep. 2000;339(1):1–77.
  • Metzler R, Klafter J. The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics. J Phys A Math General. 2004;37(31):R161–R208.
  • Podlubny I. Fractional differential equations. San Diego: Academic Press; 1999.
  • Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Amsterdam: Elsevier; 2006.
  • Klafter J, Lim SC, Metzler R. eds. Fractional dynamics: recent advances. Singapore: World Scientific Publishing; 2012.
  • Nonnenmacher TF, Nonnenmacher DJF. Towards the formulation of a nonlinear fractional extended irreversible thermodynamics. Acta Phys Hung . 1989;66(1-4):145–154.
  • Kadem A, Baleanu D. Fractional radiative transfer equation within chebyshev spectral approach. Comput Math Appl. 2010;59(5):1865–1873.
  • Espinosa-Paredes G, Polo-Labarrios M-A, Espinosa-Martínez E-G, et al. Fractional neutron point kinetics equations for nuclear reactor dynamics. Ann Nucl Energy. 2011;38(2-3):307–330.
  • Espinosa-Paredes G, Vázquez-Rodríguez A, Polo-Labarrios M-A, et al. The transient heat transfer of a pebble fuel considering anomalous diffusion. Energy Sources A. 2014;36(3):284–291.
  • Pomraning GC. An extension of the Eddington approximation. J Quantitative Spectroscopy Radiative Transfer. 1969;9:407–422.
  • Deghiedy AR, Sallah M, Abdou MA. Radiative transfer in random media with Rayleigh scattering. J Quantitative Spectroscopy Radiative Transfer. 2003;76:359–372.
  • Gorenflo R, Kilbas AA, Mainardi F, et al. Mittag–Leffler functions, related topics and applications. Berlin: Springer-Verlag; 2014.
  • Mengüç MP, Viskanta R. Comparison of radiative transfer approximations for a highly forward scattering planar medium. J Quantitative Spectroscopy Radiative Transfer. 1983;29:381–394.
  • Agrawal OP. Fractional variational calculus in terms of Riesz fractional derivatives. J Phys A Math Theor. 2007;40:6287–6303.
  • Jumarie G. On the fractional solution of the equation f(x + y)=f(x)f(y) and its application to fractional transform. Appl Math Comput. 2012;219:1625–1643.
  • Jumarie G. An approach to differential geometry of fractional order via modified Riemann–Liouville derivative. Acta Math Sin. 2012;28:1741–1768.
  • Agrawal OP, Muslih SI, Baleanu D. Generalized variational calculus in terms of multi-parameters fractional derivatives. Commun Nonlinear Sci Numer Simul. 2011;16:4756–4767.
  • Agrawal OP. Formulation of Euler–Lagrange equations for fractional variational problems. J Math Anal Appl. 2002;272:368–379.

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