[1] A. Aldoghaither, D.Y. Liu and T.M. Laleg-Kirati, Modulating functions based algorithm for the estimation of the coefficients and differentiation order for a space-fractional advection-dispersion equation, SIAM J. Sci. Comput. 37 (2015) 2813–2839.
[2] S.R. Arridge and J.C. Schotland, Optical tomography: forward and inverse problems, Inverse Probl. 25 (2009) 123010.
[3] A. Babaei and S. Banihashemi, A stable numerical approach to solve a time-fractional inverse heat conduction problem, Iran J. Sci. Technol. Trans. Sci. 42 (2018) 2225–2236.
[4] A. Babaei and S. Banihashemi, Reconstructing unknown nonlinear boundary conditions in a time-fractional inverse reaction–diffusion–convection problem, Numer. Methods Part. Differ. Equ. 35 (2018) 976–992.
[5] D. Baleanu, J.A. Tenreiro Machado, A.C.J. Luo, Fractional Dynamics and Control, Springer, New York, 2012.
[6] J.V. Beck, B. Blackwell and C.R. Clair, Inverse Heat Conduction: Ill-Posed Problems, New York, 1985.
[7] A.S. Chaves, A fractional diffusion equation to describe Levy flights, Phys. Lett. A 239 (1998) 13–16.
[8] F.F. Dou and Y.C. Hon, Numerical computation for backward time-fractional diffusion equation, Eng. Anal. Boundary Elem. 40 (2014) 138–146.
[9] D.N. Ghosh Roy and L.S. Couchman, Inverse Problems and Inverse Scattering of Plane Waves, Academic Press, New York, 2002.
[10] R. Gorenflo, F. Mainardi, D. Moretti, G. Pagnini and P. Paradisi, Fractional diffusion: probability distributions and random walk models, Phys. A 305 (2002) 106–112.
[11] B.I. Henry and S.L. Wearne, Fractional reaction–diffusion, Phys. A 276 (2000) 448–455.
[12] H. Jafari, K. Sayevand, H. Tajadodi and D. Baleanu, Homotopy analysis method for solving Abel differential equation of fractional order, Cent. Eur. J. Phys. 11 (2013) 1523–1527.
[13] B. Jin and W. Rundell, A tutorial on inverse problems for anomalous diffusion processes, Inverse Probl. 31 (2015) 035003.
[14] B. Jin and W. Rundell, An inverse problem for a one-dimensional time-fractional diffusion problem, Inverse Probl. 28 (2012) 075010.
[15] Y. Luchko, W. Rundell, M. Yamamoto and L. Zuo, Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction-diffusion equation, Inverse Probl. 29 (2013) 065019.
[16] M.M. Meerschaert and C. Tadjeran, Finite difference approximations for fractional advection-dispersion flow equations, J. Comput. Appl. Math. 172 (2004) 65–77.
[17] R. Metzler and J. Klafter, The random walk’s guide to anomalous diffusion: A fractional dynamics approach, Phys. Rep. 339 (2000) 1–77.
[18] D.A. Murio, Mollification and space marching, K. Woodbury (Ed.), Inverse Engineering Handbook, CRC Press, Boca Raton, FL, (2002).
[19] D.A. Murio, On the stable numerical evaluation of Caputo fractional derivatives, Comput. Math. Appl. 51 (2006) 1539–1550.
[20] D.A. Murio, Time fractional IHCP with Caputo fractional derivatives, Comput. Math. Appl. 56 (2008) 2371–2381.
[21] K.B. Oldham and J. Spanier, The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order, Academic Press, New York, 1974.
[22] V. Penenko, A. Baklanov, E. Tsvetova and A. Mahura, Direct and inverse problems in a variational concept of environmental modeling, Pure Appl. Geophys. 169 (2012) 447–465.
[23] C.M.A. Pinto, A.R.M. Carvalho, A latency fractional order model for HIV dynamics, J. Comput. Appl. Math. 312 (2017) 240–256.
[24] I. Podlubny, Fractional Differential Equations, Academic Press, New York, 1999.
[25] M. Prato and L. Zanni, Inverse problems in machine learning: an application to brain activity interpretation, J. Phys. Conf. Ser. 135 (2008) 012085.
[26] E. Scalas, R. Gorenflo and F. Mainardi, Fractional calculus and continuous-time finance, Phys. A 284 (2000) 376–384.
[27] K. Seki, M. Wojcik and M. Tachiya, Fractional reaction–diffusion equation, J. Chem. Phys. 119 (2003) 2165–2174.
[28] X. Song, G. Zheng and L. Jiang, Recovering the reaction coefficient for two-dimensional time fractional diffusion equations, (2017),- arXiv:1707.00671 [math.NA].
[29] C. Sun, G. Li, and X. Jia, Simultaneous inversion for the diffusion and source coefficients in the multi-term TFDE, Inverse Probl. Sci. Eng. 25 (2017) 1–21.
[30] A. Taghavi, A. Babaei, A. Mohammadpour, A stable numerical scheme for a time-fractional inverse parabolic equation, Inverse Probl. Sci. Eng. 25 (2017) 1474–1491.
[31] D. Trucu, D.B. Ingham and D. Lesnic, Inverse space-dependent perfusion coefficient identification, J. Phys. Conf. Ser. 135 (2008) 012098.
[32] V.K. Tuan, Inverse problem for fractional diffusion equation, Fract. Calc. Appl. Anal. 14 (2011) 31–55.
[33] V.K. Tuan and N.S. Hoang, An inverse problem for a multidimensional fractional diffusion equation, Anal. 36 (2016) 107–122.
[34] N.H. Tuan, L.D. Long, V.T. Nguyen and T. Tran, On a final value problem for the time-fractional diffusion equation with inhomogeneous source, Inverse Probl. Sci. Eng. 25 (2017) 1367–1395.
[35] T. Wei and Z.Q. Zhang, Reconstruction of a time-dependent source term in a time-fractional diffusion equation, Eng. Anal. Boundary Elem. 37 (2013) 23–31.
[36] L. Yan and F. Yang, Efficient Kansa-type MFS algorithm for time-fractional inverse diffusion problems, Comput.Math. Appl. 67 (2014) 1507–1520.
[37] X.J. Yang, Advanced Local Fractional Calculus and its Applications, World Science Publisher LLC, New York, USA, 2012.
[38] G.H. Zheng and T. Wei, Spectral regularization method for the time fractional inverse advection-dispersion equation,J. Comput. Appl. Math. 233 (2010) 2631–2640.
[39] Y. Zhou, Basic Theory of Fractional Differential Equations, World Scientific, Singapore, 2014.
International Journal of Nonlinear Analysis and Applications
)