[1] S.G. Bankoff, Heat conduction or diffusion with change of phase, Adv. Chem. Engin. 5 (1964), 75–150.
[2] H. Capart, M. Bellal and D.L. Young, Self-similar evolution of semi-infinite alluvial channels with moving boundaries, J. Sedimentary Res. 77 (2007), no. 1, 13–22.[3] J. Crank and J. Crank, Free and moving boundary problems, Oxford University Press, USA, 1984.
[4] M. Cui, Compact finite difference method for the fractional diffusion equation, J. Comput. Phys. 228 (2009), no.
20, 7792–7804.
[5] B.A. Finlayson, The method of weighted residuals and variational principles, volume 87 of Mathematics in Scienceand Engineering, SIAM, 1972.
[6] R.S. Gupta and N.C. Banik, Constrained integral method for solving moving boundary problems, Comput. Meth.
Appl. Mmech. Engin. 67 (1988), no. 2, 211–221.
[7] R.S. Gupta and N.C. Banik. Solution of a weakly two-dimensional melting problem by an approximate method, J.
Comput. Appl. Math. 31 (1990), no. 3, 351–356.
[8] Z. Hammouch and T. Mekkaoui. Travelling-wave solutions for some fractional partial differential equation by
means of generalized trigonometry functions. Int. J. Appl. Math. Res. 1 (2012), no. 1, 206–212.
[9] J.H. He. Approximate analytical solution for seepage flow with fractional derivatives in porous media, Comput.
Meth. Appl. Mech. Engin. 167 (1998), no. 1-2, 57–68.
[10] Y.C. Hon and T. Wei, The method of fundamental solution for solving multidimensional inverse heat conduction
problems, CMES Comput. Model. Eng. Sci. 7 (2005), no. 2, 119–132.
[11] M. Inokuti, H. Sekine and T. Mura, General use of the Lagrange multiplier in nonlinear mathematical physics,
Var. Method Mech. Solids 33 (1978), no. 5, 156–162.
[12] G. Jumarie, Table of some basic fractional calculus formulae derived from a modified Riemann–Liouville derivative
for non-differentiable functions, Appl. Math. Lett. 22 (2009), no. 3, 378–385.
[13] G. Jumarie, An approach via fractional analysis to non-linearity induced by coarse-graining in space, Nonlinear
Anal. Real World Appl. 11 (2010), no. 1, 535–546.
[14] G. Jumarie, On the fractional solution of the equation f(x + y) = f(x)f(y) and its application to fractional
Laplace’s transform, Appl. Math. Comput. 219 (2012), no. 4, 1625–1643.
[15] A.A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and applications of fractional differential equations, Elsevier, 2006.
[16] D. Lesnic and L. Elliott, The decomposition approach to inverse heat conduction, J. Math. Anal. Appl. 232 (1999),
no. 1, 82–98.
[17] J.C. Muehlbauer, Heat conduction with freezing or melting, Appl. Mech. Rev. 18 (1965), 951.
[18] Z. Odibat and S. Momani, A generalized differential transform method for linear partial differential equations of
fractional order, Appl. Math. Lett. 21 (2008), no. 2, 194–199.
[19] K.N. Rai and S. Das, Numerical solution of a moving-boundary problem with variable latent heat, Int. J. Heat
Mass Transfer 52 (2009), no. 7-8, 1913–1917.
[20] Rajeev, Homotopy perturbation method for a Stefan problem with variable latent heat. Thermal Sci. 18 (2014),
no. 2, 391–398.
[21] H. Rasmussen, An approximate method for solving two-dimensional Stefan problems, Lett. Heat Mass Transfer 4
(1977), no. 4, 273–277.
[22] J.J. Trujillo, E. Scalas, K. Diethelm and D. Baleanu. Fractional calculus: Models and numerical methods, World
Scientific, 2016.
[23] V.R. Voller, J.B. Swenson, W. Kimn and C. Paola, An enthalpy method for moving boundary problems on the
earth’s surface, Int. J. Numerical Meth. Heat Fluid Flow 16 (2006), no. 5, 641–654.
[24] S. Wang and P. Perdikaris. Deep learning of free boundary and Stefan problems, J. Comput. Phys. 428 (2021),
109914.
[25] H. Wang and T.C. Xia, The fractional supertrace identity and its application to the super Jaulent–Miodek hierarchy, Commun. Nonlinear Sci. Numerical Simul. 18 (2013), no. 10, 2859–2867.
[26] G.W. Wang, X.Q. Liu and Y.Y. Zhang, Lie symmetry analysis to the time fractional generalized fifth-order KdV
equation, Commun. Nonlinear Sci. Numerical Simul. 18 (2013), no. 9, 2321–2326.
[27] B.J. West, M. Bologna and P. Grigolini, Physics of fractal operators, Springer, New York, 2003.