An inverse source problem for a two terms time-fractional diffusion equation
DOI:
https://doi.org/10.5269/bspm.45265Abstract
In this paper, we consider an inverse problem for a linear heat equation involving two time-fractional derivatives, subject to a nonlocal boundary condition. We determine a source term independent of the space variable, and the temperature distribution with an over- determining function of integral type.
References
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10. Z. Li, Y. Liu and M. Yamamoto, Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients, Appl. Math. Comput., 257, 381-397, (2015). https://doi.org/10.1016/j.amc.2014.11.073
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12. Y. Luchko and R. Gorenflo, An operational method for solving fractional differential equations with the Caputo derivatives, Acta Math. Vietnam, 24, 207-233, (1999).
13. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, New York and London, (1993).
2. V. Daftardar-Gejji and S. Bhalekar, Boundary value problems for multi-term fractional differential equations, J. Math. Anal. Appl., 345, 754-765, (2008). https://doi.org/10.1016/j.jmaa.2008.04.065
3. V. A. Il'in, How to express basis conditions and conditions for the equiconvergence with trigonometric series of expansions related to non-self-adjoint differential operators, Computers and Mathematics with Applications, 34, 641-647, (1997). https://doi.org/10.1016/S0898-1221(97)00160-0
4. V. Isakov, Inverse problems for partial differential equations (Second edition), Springer, New York, (2006).
5. M. I. Ismailov, F. Kanca and D. Lesnic, Determination of a time-dependent heat source under nonlocal boundary and integral overdetermination conditions, Appl. Math. Comp., 218, 4138-4146, (2011). https://doi.org/10.1016/j.amc.2011.09.044
6. V. L. Kamynin, On the inverse problem of determining the right-hand side of a parabolic equation under an integral overdetermination condition, Mathematical Notes, 77(4), 482-493, (2005). https://doi.org/10.1007/s11006-005-0047-6
7. M. V. Keldysh, On the completeness of the eigenfunctions of some classes of non-selfadjoint linear operators, Russ. Math. Surv. 26(4), (1971), https://doi.org/10.1070/RM1971v026n04ABEH003985
8. A. A. Kilbas, H.M. Srivastava and J.J. Trujillo, Theory and Applications of Fractional Differential Equations, Elsevier, Amsterdam, (2006).
9. M. Kirane, S. A. Malik and M. A. Al-Gwaiz, An inverse source problem for a two dimensional time fractional diffusion equation with nonlocal boundary conditions, Math. Meth. Appl. Sci., 36, 1056-1069, (2013). https://doi.org/10.1002/mma.2661
10. Z. Li, Y. Liu and M. Yamamoto, Initial-boundary value problems for multi-term time-fractional diffusion equations with positive constant coefficients, Appl. Math. Comput., 257, 381-397, (2015). https://doi.org/10.1016/j.amc.2014.11.073
11. Y. Liu, Strong maximum principle for multi-term time-fractional diffusion equations and its application to an inverse problem, Computers and Mathematics with Applications, 73, 96-108, (2017). https://doi.org/10.1016/j.camwa.2016.10.021
12. Y. Luchko and R. Gorenflo, An operational method for solving fractional differential equations with the Caputo derivatives, Acta Math. Vietnam, 24, 207-233, (1999).
13. S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science Publishers, New York and London, (1993).
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2021-12-17
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