fractional diffusion-wave equation, nonlocal problem, necessary nonlocal conditions, problem with integral conditions, fractional derivative of Gerasimov–Caputo
Abstract:
The paper studies a fractional diffusion-wave equation with a fractional derivative in the sense of Garasimov–Caputo. In terms of integral operators associated with the fractional diffusion-wave equation, the necessary nonlocal conditions are written out, which connect the traces of the solution under study and its derivatives on the boundary of a rectangular region. Based on this property, the unique solvability of the problem with nonlocal internal and boundary conditions is proven. The solution is obtained in explicit form.
Keywords:fractional diffusion-wave equation, nonlocal problem, necessary nonlocal conditions, problem with integral conditions, fractional derivative of Gerasimov–Caputo
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