An inverse time-dependent source problem for a time-fractional diffusion equation with nonlocal boundary conditions

Mihoubi, Farid and Nouiri, Brahim (2024) An inverse time-dependent source problem for a time-fractional diffusion equation with nonlocal boundary conditions. Miskolc Mathematical Notes, 25 (2). pp. 855-870. ISSN 1787-2413

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Abstract

In this paper, we investigate an inverse time-dependent source problem for a time-fractional diffusion equation with nonlocal boundary and integral over-determination conditions. The fractional derivative is described in the generalized Caputo sense. The nonlocal boundary conditions are regular but not strongly regular. The special thing about this problem is: the system of eigenfunctions is not complete, but the system of eigen-and associated functions forming a basis in L2 (0,1). Under some natural regularity and consistency conditions on the input data the existence, uniqueness and continuously dependence upon the data of the solution are shown by using the generalized Fourier method, the estimates of Mittag-Leffler function and Banach’s contraction mapping principle.

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