Stability of the time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative
Stability of the time-dependent identification problem for a fractional Telegraph equation with the Caputo derivative
DOI:
https://doi.org/10.52754/16948645_2023_2_166Keywords:
The telegraph equation, Hilbert space, self-adjoint, positive operator, Caputo derivativeAbstract
The telegraph equation , in a Hilbert space is investigated. Here is a self-adjoint, positive operator, is the Caputo derivative. An inverse problem is considered in which, along with , also a time varying factor of the source function is unknown. To solve this inverse problem, we take the additional condition with an arbitrary bounded linear functional .Existence and uniqueness theorem for the solution to the problem under consideration is proved. Inequalities of stability are obtained.
References
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Ashyralyev.A., Al-Hazaimeh.M. Stability of the time-dependent identication problem for the Telegraph equation with involution, International Journal of Applied Mathematics, 35, 3, 447--459 ,(2022). DOI: https://doi.org/10.12732/ijam.v35i3.7
Cascaval. R., Eckstein.E., Frota.C., Goldstein.A.,, Fractional telegraph equations, J. Math. Anal. Appl. 276, 145-159 (2002). DOI: https://doi.org/10.1016/S0022-247X(02)00394-3
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