Inverse problem of determining a temporary source in the heat equation with time-fractional derivatives
Inverse problem of determining a temporary source in the heat equation with time-fractional derivatives
DOI:
https://doi.org/10.52754/16948645_2023_2_6Keywords:
inverse problem, Cauchy problem, Gerasimov–Caputo fractional derivative, Mittag–Leffler function, integral equation..Abstract
The paper investigates the inverse problem of determining the unknown time-dependent source in the Cauchy problem for the diffusion equation with time-fractional derivatives with redefinition at the point x = 0. To solve the inverse problem
the fundamental solution of the diffusion equation with time-fractional derivatives is used. The inverse problem is reduced to an equivalent linear Volterra integral equation of the second kind. Using the method of successive approximations, we prove the existence and uniqueness of a solution to the problem under consideration. A stability estimate is also obtained.
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