Issue
Math. Model. Nat. Phenom.
Volume 16, 2021
Fractional Dynamics in Natural Phenomena
Article Number 39
Number of page(s) 28
DOI https://doi.org/10.1051/mmnp/2021022
Published online 15 June 2021
  1. A. Atangana and D. Baleanu, New fractional derivatives with non-local and non-singular kernel: theory and application to heat transfer model. Thermal Sci. 20 (2) (2016) 763–769. [CrossRef] [Google Scholar]
  2. T.M. Atanackovic, S. Pilipovic and D. Zorika, Properties of the Caputo-Fabrizio fractional derivative and its distributional settings. Fract. Calc. Appl. Anal. 21 (2018) 29–44. [CrossRef] [Google Scholar]
  3. D. Baleanu, K. Diethlem, E. Scalas and J.J. Trujillo, Fractional calculus. Models and Numerical Methods, Series on Complexity, Nonlinearity and Chaos, vol. 3, World Scientific (2011). [Google Scholar]
  4. G.A.M. Boro Nchama, Properties of Caputo-Fabrizio fractional operators. NTMSCI 8 (2020) 1–25. [CrossRef] [Google Scholar]
  5. M. Caputo, Elasticita e Dissipazione. Zanichelli, Bologna (1965). [Google Scholar]
  6. M. Caputo and M. Fabrizio, A new definition of fractional derivative without singular kernel. Progr. Fract. Differ. Appl. 1 (2015) 73–85. [Google Scholar]
  7. M. Caputo and M. Fabrizio, Applications of new time and spatial fractional derivatives with exponential kernels. Progr. Fract. Differ. Appl. 2 (2016) 1–11. [CrossRef] [Google Scholar]
  8. R. Gorenflo, A.A. Kilbas, F. Mainardi and S.V. Rogosin, Mittag-Leffler Functions Related Topics and Applications, Springer, Heildelberg (2014). [Google Scholar]
  9. E.C. Grigoletto, E.C. Oliveira and R.F. Camargo, Integral representations of Mittag-Leffler function on the positive real axis. Tendencias Matematica Aplicada e Computacional 20 (2019) 217–228. [CrossRef] [Google Scholar]
  10. H.J. Haubold, A.M. Mathai and R.K. Saxena, Mittag-Leffler functions and their applications. J. Appl. Math. 2011 (2011) 298628, 51 pages. [CrossRef] [Google Scholar]
  11. J. Hristov, Linear viscoelastic responses and constitutive equations in terms of fractional operators with non-singular kernels. Pragmatic approach, memory kernel correspondence requirement and analyses. Eur. Phys. J. Plus 134 (2019) 283. [Google Scholar]
  12. J. Hristov, On the Atangana–Baleanu derivative and its relation to the fading memory concept: the diffusion equation formulation, in Fractional Derivatives with Mittag-Leffler Kernel, Studies in Systems, Decision and Control 194, edited by J.F. Gómez et al. Springer Nature Switzerland AG (2019). [Google Scholar]
  13. J. Kacur and R. Van Keer, Solution of contaminant transport with adsorption in porous media by the method of characteristics. Math. Modelling Num. Anal. 35 (2001) 981–1006. [CrossRef] [Google Scholar]
  14. D. Kumar, J. Singh, K. Tanwar and D. Baleanu, A new fractional exothermic reactions model having constant heat source in porous media with power, exponential and Mittag-Leffler laws. Int. J. Heat Mass Transfer 138 (2019) 1222–7. [CrossRef] [Google Scholar]
  15. S. Kumar, S. Ghosh, B. Samet and E.F.D. Goufo, An analysis for heat equations arises in diffusion process using new Yang-Abdel-Aty-Cattani fractional operator. Math. Meth. Appl. Sci. 43 (2020) 6062–6080. [CrossRef] [Google Scholar]
  16. H. Kurikami, A. Malins, M. Takeishi, K. Saito and K. Iijima, Coupling the advection-dispersion equation with fully kinetic reversible/irreversible sorption terms to model radiocesium soil profiles in PlaceNameplaceFukushima PlaceTypePrefecture. J. Environ. Radioactivity 171 (2017) 99–109. [CrossRef] [Google Scholar]
  17. M. Kurulay and M. Bayram, Some properties of the Mittag-Leffler functions and their relation with the Wright functions. Adv. Differ. Eqs. 2012 (2012) 181. [CrossRef] [Google Scholar]
  18. S. Lee, D.J. Kim and J.W. Choi, Comparison of first-order sorption kinetics using concept of two-site sorption model. Environ. Eng. Sci. 29 (2012) 1002–1007. [CrossRef] [PubMed] [Google Scholar]
  19. F.J. Leij and M. Th. Vn Genuchten, Solute transport, in Soil Physics Companion, edited by A.W. Warrick. CRC Press, Boca Raton FL (2002) 189–240. [Google Scholar]
  20. C.F. Lorenzo and T.T. Hartley, Generalized functions for the fractional calculus. NASA/TP-1999- 209424/REV1. [Google Scholar]
  21. Y. Liu, F.Zong and L. Zheng, The analysis solutions for two-dimensional fractional diffusion equations with variable coefficients. Int. J. Math. Trends Technol. 5 (2014) 60–66. [CrossRef] [Google Scholar]
  22. Y.U. Luchko, Operational method in fractional calculus. Fract. Calc. Appl. Anal. 2 (1999) 463–488. [Google Scholar]
  23. Y. Luchko, On some new properties of the fundamental solution to the multi-dimensional space- and time-fractional diffusion-wave equation. Mathematics 5 (2017) 76. [CrossRef] [Google Scholar]
  24. Y. Povstenko and T. Kyrylych, Two approaches to obtaining the space-time fractional advection-diffusion equation. Entropy 19 (2017) 297. [CrossRef] [Google Scholar]
  25. J.L. Schiff, The Laplace Transform: Theory and Applications. Springer Verlag, New York (1999). [CrossRef] [Google Scholar]
  26. B. Stankovic, On the function E.M. Wright. Publications de L’Institute Mathematique, Nouvelle serie, 10 (1970) 113–124. [Google Scholar]
  27. G. Uffink, A. Elfeki, M. Dekking, J. Bruining and C. Kraaikamp, Understanding the non-Gaussian nature of linear reactive solute transport in 1D and 2D. From particle dynamics to the partial differential equations. Transp. Porous Med. 91 (2012) 547–571. [Google Scholar]
  28. J.J.A. van Kooten, A method to solve the advection-dispersion equation with a kinetic adsorption isotherm. Adv. Water Res. 19 (1996) 193–206. [CrossRef] [Google Scholar]
  29. Y.S. Wu, J.B. Kool, P.S. Huyakom and Z.A. Saleem, An analytical model for nonlinear adsorptive transport through layered soils. Water Resour. Res. 33 (1997) 21–29. [CrossRef] [Google Scholar]

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