Abbaszadeh, M. and Dehghan, M. Numerical and analytical investi-gations for solving the inverse tempered fractional diffusion equation via interpolating element-free Galerkin (IEFG) method, J. Therm. Anal. Calorim. 143(3) (2021), 1917–1933.
 Abdelkawy, M.A., Babatin, M.M., Alnahdi, A.S. and Taha, T.M. Leg-endre spectral collocation technique for fractional inverse heat conduction problem, Int. J. Mod. Phys. C. 33(05) (2022), 2250065.
 Ait Ben Hassi, E.M., Chorfi, S.E. and Maniar, L. Identification of source terms in heat equation with dynamic boundary conditions, Math. Meth-ods Appl. Sci. 45(4) (2022), 2364–2379.
 Alpar, S. and Rysbaiuly, B. Determination of thermophysical character-istics in a nonlinear inverse heat transfer problem, Appl. Math. Comput. 440 (2023), 127656.
 Badia, A.E. and Duong, T.H. On an inverse source problem for the heat equation: application to a detection problem, J. Inverse Ill-Posed Probl. 10 (2002), 585–589.
 Bal, G. and Schotland, J.C. Inverse scattering and acousto-optic imag-ing, Phys. Rev. Lett. 104(4) (2010), 043902.
 Baraniuk, R. and Steeghs, P. Compressive radar imaging, Radar con-ference, Boston (MA): IEEE (2007), 128–133.
 Bondarenko, N.P. Finite-difference approximation of the inverse Sturm–Liouville problem with frozen argument, Appl. Math. Comput. 413 (2022), 126653.
 Ciofalo, M. Solution of an inverse heat conduction problem with third-type boundary conditions, Int. J. Therm. Sci. 175 (2022), 107466.
 Crossen E., Gockenbach M.S., Jadamba, B., Khan, A.A. and Winkler, B. An equation error approach for the elasticity imaging inverse problem for predicting tumor location, Comput. Math. Appl. 67(1) (2014), 122–135.
 Djennadi, S., Shawagfeh, N., Osman, M.S., Gomez-Aguilar, J.F. and Arqub, O.A. The Tikhonov regularization method for the inverse source problem of time fractional heat equation in the view of ABC-fractional technique, Phys. Scr. 96(9) (2021), 094006.
 Gu, Y., Lei, J., Fan, C.M. and He, X.Q. The generalized finite difference method for an inverse time-dependent source problem associated with three-dimensional heat equation, Eng. Anal. Bound. Elem. 91 (2018), 73–81.
 Gu, Y., Wang, L., Chen, W., Zhang, C. and He, X. Application of the meshless generalized finite difference method to inverse heat source problems, Int. J. Heat Mass Transf. 108 (2017), 721–729.
 Hajishafieiha, J. and Abbasbandy, S. Numerical solution of two-dimensional inverse time-fractional diffusion problem with non-local boundary condition using a-polynomials, J. Appl. Math. Comput. 69(2) (2023), 1945–1965.
 Huang, D.Z., Huang, J., Reich, S. and Stuart, A.M. Efficient derivative-free Bayesian inference for large-scale inverse problems, Inverse Probl. 38(12) (2022), 125006.
 Huntul, M.J. Space-dependent heat source determination problem with nonlocal periodic boundary conditions, Results Appl. Math. 12 (2021),100223.
 Huntul, M.J. Recovering a source term in the higher-order pseudo-parabolic equation via cubic spline functions, Phys. Scr. 97(3) (2022), 035004.
 Ikehata, M. An inverse source problem for the heat equation and the enclosure method, Inverse Probl. 23 (2007), 183–202.
 Isakov, V. and Wu, S.F. On theory and application of the Helmholtz equation least squares method in inverse acoustics, Inverse Probl. 18(4) (2002), 1147.
 Johansson, B.T. and Lesnic, D. A variational method for identifying a spacewise-dependent heat source, IMA J. Appl. Math. 72(6) (2007), 748–760.
 Johansson, T. and Lesnic, D. Determination of a spacewise dependent heat source, J. Comput. Appl. Math. 209(1) (2007), 66–80.
 Kilicman, A. and Al Zhour, Z.A.A. Kronecker operational matrices for fractional calculus and some applications, Appl. Math. Comput. 187(1) (2007), 250–265.
 Li, Y. and Hu, X. Artificial neural network approximations of Cauchy in-verse problem for linear PDEs, Appl. Math. Comput. 414 (2022), 126678.
 Lin, J. and Liu, C.S. Recovering temperature-dependent heat conductiv-ity in 2D and 3D domains with homogenization functions as the bases, Eng. Comput. 38(3) (2022), 2349–2363.
 Lu, Z.R., Pan, T., and Wang, L. A sparse regularization approach to inverse heat source identification, Int. J. Heat Mass Transf. 142 (2019), 118430.
 Mahmoudi, M., Shojaeizadeh, T. and Darehmiraki, M. Optimal control of time-fractional convection-diffusion-reaction problem employing com-pact integrated RBF method, Math. Sci. (Springer) 17(1) (2023), 1–14.
 Mishra, S. and Molinaro, R. Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs, IMA J. Numer. Anal. 42(2) (2022), 981–1022.
 Nawaz Khan, M., Ahmad, I. and Ahmad, H. A radial basis function collocation method for space-dependent inverse heat problems, J. Appl. Comput. Mech. (2020).
 Qiu, L., Lin, J., Wang, F., Qin, Q.H. and Liu, C.S. A homogenization function method for inverse heat source problems in 3D functionally graded materials, Appl. Math. Model. 91 (2021), 923–933.
 Rezazadeh, A., Mahmoudi, M. and Darehmiraki, M. A solution for fractional PDE constrained optimization problems using reduced basis method, Comput. Appl. Math. 39(2) (2020), 1–17.
 Saadatmandi, A. and Dehghan, M. A new operational matrix for solv-ing fractional-order differential equations, Comput. Math. Appl. 59(3) (2010), 1326–1336.
 Shojaeizadeh, T., Mahmoudi, M. and Darehmiraki, M. Optimal control problem of advection-diffusion-reaction equation of kind fractal-fractional applying shifted Jacobi polynomials, Chaos Solit. Fractals. 143 (2021), 110568.
 Wang, W., Han, B. and Yamamoto, M. Inverse heat problem of de-termining time-dependent source parameter in reproducing kernel space, Nonlinear Anal. Real World Appl. 14(1) (2013), 875–887.
 Wen, J., Liu, Z.X. and Wang, S.S. Conjugate gradient method for si-multaneous identification of the source term and initial data in a time-fractional diffusion equation, Appl. Math. Sci. Eng. 30(1) (2022), 324–338.
 Widrow, B. and Walach, E. Adaptive inverse control, reissue edition: a signal processing approach, John Wiley and Sons, 2008.
 Yang, F. and Fu, C.L. A mollification regularization method for the inverse spatial-dependent heat source problem, J. Comput. Appl. Math. 255 (2014), 555–567.
 Yang, S. and Xiong, X. A Tikhonov regularization method for solving an inverse heat source problem, Bull. Malays. Math. Sci. Soc. 43(1) (2020), 441–452.