Abstract
We study the inverse problem for a differential equation of order (Figure presented.) with the time Caputo fractional derivative and a source with values in Schwartz-type distributions. The generalized solution of the Cauchy problem for such an equation with initial values and a time-dependent reaction coefficient are unknown. We find sufficient conditions for the unique solvability of the inverse problem under a time- and space-integral overdetermination conditions.
Original language | British English |
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Pages (from-to) | 16381-16393 |
Number of pages | 13 |
Journal | Mathematical Methods in the Applied Sciences |
Volume | 46 |
Issue number | 15 |
DOIs | |
State | Published - Oct 2023 |
Keywords
- fractional derivative
- Green vector-function
- integral condition
- inverse problem
- Schwartz distribution