ANALYSIS OF THE 1D FRACTIONAL DIFFUSION EQUATION WITH INITIAL-BOUNDARY PROBLEM
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Аннотация
In this paper, we consider one-dimensional time-fractional diffusion equation is bounded domain. In this work, we have seen the existence of a solution of the 1st initial boundary value problem for the one-dimensional diffusion equation. It is proved that the solution of problem (1)-(5) exists and is unique. First, we give a definition of the classical solution of the direct problem. Then we studied its features. In the
process of solving the equation, we used Foure's method, Mittag-Liffler function, Caputo fractional derivatives, Laplace transforms for Caputo fractional derivative. Finally, we directly show that the solution of the problem exists and is unique.
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