[1] Abdollahi, N. and Rostamy, D. Identifying an unknown time-dependent boundary source in
time-fractional diffusion equation with a non-local boundary condition, J. Comput. Appl.
Math., 355 (2019), 36–50.
[2] Ali, M. and Aziz, S. Some inverse problems for time-fractional diffusion equation with
nonlocal Samarskii–Ionkin type condition, Math. Methods Appl. Sci., 44 (2021), 8447–8462.
[3] Arridge, S., Maas, P., Öktem, O. and Schönlieb, C.B. Solving inverse problems using data-
driven models, Acta Numer., 28 (2019), 1–174.
[4] Bazan, F., Bedin, L., Ismailov, M.I. and Borges, L. Inverse time-dependent source problem
for the heat equation with a nonlocal Wentzell–Neumann boundary condition, Netw. Heterog.
Media, 18 (2023), 1747–1771.
[5] Beckers, S. and Yamamoto, M. Regularity and unique existence of solution to linear diffusion
equation with multiple time-fractional derivatives, In Control and Optimization with PDE
Constraints, Springer, (2013), 45–55.
[6] Błasik, M. Numerical scheme for a two-term sequential fractional differential equation, Sci.
Res. Inst. Math. Comput. Sci., 10(2) (2011), 17–29.
[7] Brandibur, O. and Kaslik, É. Stability properties of multi-term fractional-differential equa-
tions, Fractal Fract., 7(2) (2023), 117.
[8] Chen, J., Liu, F. and Anh, V. Analytical solution for the time-fractional telegraph equation
by the method of separating variables, J. Math. Anal. Appl., 338(2) (2008), 1364–1377.
[9] Chung, J. and Gazzola, S. Computational methods for large-scale inverse problems: a survey
on hybrid projection methods, SIAM Rev., 66(2) (2024), 205–284.
[10] D’Abbicco, M. and Girardi, G. Asymptotic profile for a two-terms time fractional diffusion
problem. Fract. Calc. Appl. Anal. 25(3) (2022), 1199–1228.
[11] D’Abbicco, M. and Girardi, G. Decay estimates for a perturbed two-terms space-time frac-
tional diffusive problem, Evol. Equ. Control Theory, 12(4) (2023), 1106–1138.
[12] Derbissaly, B., Kirane, M. and Sadybekov, M.A. Inverse source problem for two-term time-
fractional diffusion equation with nonlocal boundary conditions, Chaos Solitons Fractals, 183
(2024), 114897.
[13] Dib, F. and Kirane, M. An inverse source problem for a two terms time-fractional diffusion
equation, Bol. Soc. Parana. Mat., 2022 (2022) 1–15.
[14] Ding, M.H., Liu, H. and Lo, C.W. Inverse problems for coupled nonlocal nonlinear systems
arising in mathematical biology, arXiv preprint arXiv:2407.15713, 2024.
[15] Fazli, H., Bahrami, F. and Shahmorad, S. Extremal solutions for multi-term nonlinear frac-
tional differential equations with nonlinear boundary conditions, Comput. Methods Differ.
Equ., 11(1) (2023), 32–41.
[16] Furati, K.M., Iyiola, O.S. and Kirane, M. An inverse problem for a generalized fractional
diffusion, Appl. Math. Comput., 249 (2014), 24–31.
[17] Hazanee, A., Lesnic, D., Ismailov, M.I. and Kerimov, N.B. Inverse time-dependent source
problems for the heat equation with nonlocal boundary conditions, Appl. Math. Comput.,
346 (2019), 800–815.
[18] Ismailov, M.I. Inverse source problem for heat equation with nonlocal Wentzell boundary
condition, Results Math., 73(2) (2018) 68.
[19] Ismailov, M.I. and Cicek, M. Inverse source problem for a time-fractional diffusion equation
with nonlocal boundary conditions, Appl. Math. Model., 40 (2016), 4891–4899.
[20] Ismailov, M.I. and Tekin, I. An inverse problem for finding the lowest term of a heat equation
with Wentzell–Neumann boundary condition, Inverse Probl. Sci. Eng., 27 (2019), 1608–1634.
[21] Jafari, H., Babaei, A. and Banihashemi, S. A novel approach for solving an inverse reaction–
diffusion–convection problem, J. Optim. Theory Appl., 183 (2019), 688–704.
[22] Khosravian-Arab, H. and Dehghan, M. A matrix approach to multi-term fractional differ-
ential equations using two new diffusive representations for the Caputo fractional derivative,
AUT J. Math. Comput., 5(4) (2024), 337–359.
[23] Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. Theory and applications of fractional dif-
ferential equations, Elsevier, 2006.
[24] Kirane, M., Malik, S.A. and Al-Gwaiz, M.A. An inverse source problem for a two dimen-
sional time fractional diffusion equation with nonlocal boundary conditions, Math. Methods
Appl. Sci., 36(9) (2013), 1056–1069.
[25] Kirane, M., Sadybekov, M.A. and Sarsenbi, A.A. On an inverse problem of reconstructing
a subdiffusion process from nonlocal data, Math. Methods Appl. Sci., 42 (2019), 2043–2052.
[26] Lattanzi, A.M. and Hrenya, C.M. A coupled, multiphase heat flux boundary condition for
the discrete element method, Chem. Eng. J., 304 (2016), 766–773.
[27] Li, T.-T. A class of non-local boundary value problems for partial differential equations and
its applications in numerical analysis, J. Comput. Appl. Math., 28 (1989), 49–62.
[28] Li, Y., Wang, T. and Gao, G.H. The asymptotic solutions of two-term linear fractional
differential equations via Laplace transform, Math. Comput. Simul., 211 (2023), 394–412.
[29] Ma, R. A survey on nonlocal boundary value problems, Appl. Math. E-Notes, 7 (2007),
257–279.
[30] Malik, S.A. and Aziz, S. An inverse source problem for a two parameter anomalous diffusion
equation with nonlocal boundary conditions, Comput. Math. Appl., 73(12) (2017), 2548–
2560.
[31] Nemati, S. and Babaei, A. A numerical method based on the Jacobi polynomials to reconstruct
an unknown source term in a time fractional diffusion-wave equation, Taiwanese J. Math.,
23(5) (2019), 1271–1289.
[32] Orazov, I. and Makhatova, A.K. On application of inverse problems with the nonlocal bound-
ary conditions in the diffusion theory, In International Conference “Functional Analysis in
Interdisciplinary Applications” (FAIA2017), Vol. 1880, AIP Publishing, (2017), 060008.
[33] Orazov, I. and Sadybekov, M.A. On a class of problems of determining the temperature
and density of heat sources given initial and final temperature, Sib. Math. J., 53(1) (2012),
146–151.
[34] Orsingher, E. and Beghin, L. Time-fractional telegraph equations and telegraph processes
with Brownian time, Probab. Theory Relat. Fields, 128(1) (2004), 141–160.
[35] Ozkan, A.S. and Adalar, İ. Inverse nodal problems for Sturm–Liouville equation with non-
local boundary conditions, J. Math. Anal. Appl., 520(1) (2023), 126904.
[36] Pal, S. and Melnik, R. Nonlocal models in biology and life sciences: sources, developments,
and applications, arXiv preprint arXiv:2401.14651, 2024.
[37] Rivlin, T.J. Chebyshev polynomials, Courier Dover Publications, 2020.
[38] Sadybekov, M.A. and Pankratova, I.N. Correct and stable algorithm for numerical solving
nonlocal heat conduction problems with not strongly regular boundary conditions, Mathe-
matics, 10(20) (2022), 3780.
[39] Stojanović, M. Existence–uniqueness result for a nonlinear n-term fractional equation, J.
Math. Anal. Appl., 353(1) (2009), 244–255.
[40] Stojanović, M. and Gorenflo, R. Nonlinear two-term time fractional diffusion-wave problem,
Nonlinear Anal. Real World Appl., 11(5) (2010), 3512–3523.
[41] Sun, L.L. and Yan, X.B. Inverse source problem for a multiterm time-fractional diffusion
equation with nonhomogeneous boundary condition, Adv. Math. Phys., 2020 (2020), 1825235.
[42] Vogel, C.R. Computational methods for inverse problems, Soc. Ind. Appl. Math., 2002.
[43] Yadigaroglu, G. and Hewitt, G.F. Introduction to multiphase flow: basic concepts, applica-
tions and modelling, Springer, 2017.
[44] Zhou, Y. and He, J.W. Well-posedness and regularity for fractional damped wave equations,
Monatsh. Math., 194 (2021), 425–458