References

  1. L. Lapidus, N.R. Amundson, Mathematics of adsorption in beds. VI. The effect of longitudinal diffusion in ion exchange and chromatographic columns, J. Phys. Chem., 56 (1952) 984–988.
  2. J.R. Philip, Numerical solution of equations of the diffusion type with diffusivity concentration-dependent, Trans. Faraday Soc., 51 (1955) 885–892.
  3. A. Ogata, R.B. Banks, A Solution of the Differential Equation of Longitudinal Dispersion in Porous Media, Geological Survey Professional Paper 411-A, United States Government Printing Office, Washington, 1961, pp. A1–A9.
  4. H. Brenner, The diffusion model of longitudinal mixing in beds of finite length. Numerical values, Chem. Eng. Sci., 17 (1962) 229–243.
  5. L.W. Gelhar, C. Welty, K.R. Rehfeldt, A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28 (1992) 1955–1974.
  6. F.T. Lindstrom, R. Haque, V.H. Freed, L. Boersma, The movement of some herbicides in soils. Linear diffusion and convection of chemicals in soils, Environ. Sci. Technol., 1 (1967) 561–565.
  7. F.J. Leij, N. Toride, M.Th. van Genuchten, Analytical solutions for non-equilibrium solute transport in three-dimensional porous media, J. Hydrol., 151 (1993) 193–228.
  8. M.A. Marino, Numerical and analytical solutions of dispersion in a finite, adsorbing porous medium, Water Resour. Bull., 10 (1974) 81–90.
  9. A. Ogata, Mathematics of Dispersion with Linear Adsorption Isotherm, Geological Survey Professional Paper 411-H, United States Government Printing Office, Washington, 1964, pp. H1–H9.
  10. A. Ogata, Theory of Dispersion in a Granular Medium, Geological Survey Professional Paper 411-I, United States Government Printing Office, Washington, 1970, I1–I34.
  11. N. Toride, F.J. Leij, M.Th. van Genuchten, The CXTFIT Code for Estimating Transport Parameters from Laboratory or Field Tracer Experiment, Version 2.0, Research Report No. 137, U.S. Salinity Laboratory, Agricultural Research Service, U.S. Department of Agriculture, Riverside, California, 1995, pp. 1–121.
  12. M.Th. van Genuchten, Analytical solutions for chemical transport with simultaneous adsorption, zero-order production and first-order decay, J. Hydrol., 49 (1981) 213–233.
  13. M.Th. van Genuchten, W.J. Alves, Analytical Solutions of the One-Dimensional Convective-Dispersive Solute Transport Equation, U.S. Department of Agriculture, Technical Bulletin No. 1661, 1982, 151 p.
  14. M.Th. van Genuchten, J.C. Parker, Boundary conditions for displacement experiments through short laboratory soil columns, Soil Sci. Soc. Am. J., 48 (1984) 703–708.
  15. M.Th. van Genuchten, P.J. Wierenga, Mass transfer studies in sorbing porous media I. Analytical solutions, Soil Sci. Soc. Am. J., 40 (1976) 473–481.
  16. F.T. Tracy, 1-D, 2-D, and 3-D analytical solutions of unsaturated flow in groundwater, J. Hydrol., 170 (1995) 199–214.
  17. A. Kumar, D.K. Jaiswal, N. Kumar, Analytical solutions of one-dimensional advection–diffusion equation with variable coefficients in a finite domain, J. Earth Syst. Sci., 118 (2009) 539–549.
  18. A. Kumar, D.K. Jaiswal, N. Kumar, Analytical solutions to one-dimensional advection–diffusion equation with variable coefficients in semi-infinite media, J. Hydrol., 380 (2010) 330–337.
  19. D.K. Jaiswal, N. Kumar, Analytical solutions of advection– dispersion equation for varying pulse type input point source in one-dimension, Int. J. Eng. Sci. Technol., 3 (2011) 22–29.
  20. A. Daga, V.H. Pradhan, Analytical solution of advection– diffusion equation in homogeneous medium, Int. J. Sci. Spirituality Bus. Technol., 2 (2013) 65–69.
  21. A. Mojtabi, M.O. Deville, One-dimensional linear advection– diffusion equation: analytical and finite element solutions, Comput. Fluids, 107 (2015) 189–195.
  22. M.L. Puri, D.A. Ralescu, Differentials of fuzzy functions, J. Math. Anal. Appl., 91 (1983) 552–558.
  23. M. Hukuhara, Intégration des applications mesurables dont la valeur est un compact convexe, Funkcial. Ekvac., 10 (1967) 205–233 (in French).
  24. O. Kaleva, Fuzzy differential equations, Fuzzy Sets Syst., 24 (1987) 301–317.
  25. S. Seikkala, On the fuzzy initial value problem, Fuzzy Sets Syst., 24 (1987) 319–330.
  26. J.J. Nieto, R. Rodríguez-López, Bounded solutions for fuzzy differential and integral equations, Chaos, Solitons Fractals, 27 (2006) 1376–1386.
  27. D. Vorobiev, S. Seikkala, Towards the theory of fuzzy differential equations, Fuzzy Sets Syst., 125 (2002) 231–237.
  28. D. O’Regan, V. Lakshmikantham, J.J. Nieto, Initial and boundary value problems for fuzzy differential equations, Nonlinear Anal., 54 (2003) 405–415.
  29. T.G. Bhaskar, V. Lakshmikantham, V. Devi, Revisiting fuzzy differential equations, Nonlinear Anal., 58 (2004) 351–358.
  30. P. Diamond, Brief note on the variation of constants formula for fuzzy differential equations, Fuzzy Sets Syst., 129 (2002) 65–71.
  31. B. Bede, S.G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations, Fuzzy Sets Syst., 151 (2005) 581–599.
  32. B. Bede, A note on “two-point boundary value problems associated with non-linear fuzzy differential equations”, Fuzzy Sets Syst., 157 (2006) 986–989.
  33. L. Stefanini, A generalization of Hukuhara difference and division for interval and fuzzy arithmetic, Fuzzy Sets Syst., 161 (2010) 1564–1584.
  34. T. Allahviranloo, Z. Gouyandeh, A. Armand, A. Hasanoglu, On fuzzy solutions for heat equation based on generalized Hukuhara differentiability, Fuzzy Sets Syst., 265 (2015) 1–23.
  35. C.V. Negoita, D.A. Ralescu, Representation theorems for fuzzy concepts, Kybernetes, 4 (1975) 169–174.
  36. R. Goetschel Jr., W. Voxman, Elementary fuzzy calculus, Fuzzy Sets Syst., 18 (1986) 31–43.
  37. B. Bede, L. Stefanini, Generalized differentiability of fuzzyvalued functions, Fuzzy Sets Syst., 230 (2013) 119–141.
  38. A. Khastan, J.J. Nieto, A boundary value problem for second order fuzzy differential equations, Nonlinear Anal., 72 (2010) 3583–3593.
  39. S.P. Mondal, T.K. Roy, Solution of second order linear differential equation in fuzzy environment, Ann. Fuzzy Math. Inf., x (2015) 1–25.
  40. B. Bede, L. Stefanini, Solution of Fuzzy Differential Equations with Generalized Differentiability using LU-Parametric Representation, X. Luo, Ed., Advances in Intelligent Systems Research, Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11), Aixles- Bains, France, 2011, pp. 785–790.
  41. C. Tzimopoulos, K. Papadopoulos, C. Evangelides, B. Papadopoulos, Fuzzy solution to the unconfined aquifer problem, Water, 11 (2019) 1–19.
  42. L. Stefanini, B. Bede, Some Notes on Generalized Hukuhara Differentiability of Interval-valued Functions and Interval Differential Equations, WP-EMS Working Papers Series in Economics, Mathematics and Statistics, WP-EMS # 2008/03, pp. 1–37. Available at: http://www.econ.uniurb.it/RePEc/urb/ wpaper/WP_12_08.pdf.
  43. B. Bede, S.G. Gal, Almost periodic fuzzy-number-valued functions, Fuzzy Sets Syst., 147 (2004) 385–403.
  44. N.A. Shah, I.L. Animasaun, R.O. Ibraheem, H.A. Babatunde, N. Sandeep, I. Pop, Scrutinization of the effects of Grashof number on the flow of different fluids driven by convection over various surfaces, J. Mol. Liq., 249 (2018) 980–990.
  45. I.L. Animasaun, R.O. Ibraheem, B. Mahanthesh, H.A. Babatunde, A meta-analysis on the effects of haphazard motion of tiny/nano-sized particles on the dynamics and other physical properties of some fluids, Chin. J. Phys., 60 (2019) 676–687.
  46. I.L. Animasaun, O.K. Koriko, B. Mahanthesh, A.S. Dogonchi, A note on the significance of quartic autocatalysis chemical reaction on the motion of air conveying dust particles, Z. Naturforsch., A: Phys. Sci., 74 (2019b) 879–904.
  47. O.K. Koriko, K.S. Adegbie, I.L. Animasaun, A.F. Ijirimoye, Comparative analysis between three-dimensional flow of water conveying alumina nanoparticles and water conveying alumina–iron(III) oxide nanoparticles in the presence of Lorentz force, Arabian J. Sci. Eng., 45 (2020) 455–464.