| Abstract: |
| The inverse problem of determining the unknown order of a fractional derivative in differential equations has been actively studied by many specialists. A number of interesting results have been obtained that have a certain applied significance. By now, the authors have investigated various modifications of this inverse problem: determining the order of the derivative or, along with the unknown order, determining some other unknown parameter or function included in the initial-boundary value problem under consideration. Analyzing the known results, we can conclude that in all these works, firstly, only the subdiffusion equation was considered and, secondly, the elliptic part of these equations has a discrete spectrum, and the authors were able to prove only the uniqueness of the solution to the inverse problem under consideration.
This report will give a brief overview of the most interesting works in this area, and will propose a new formulation and methods for solving these inverse problems. It will be proved that in the new formulation the solutions of inverse problems are not only unique, but also exist. In this case, not only the subdiffusion equations will be considered, and the elliptic parts of the equation can also have a continuous spectrum. |
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