THE SECOND BOUNDARY VALUE PROBLEM FOR A PSEUDO-PARABOLIC EQUATION OF THE THIRD ORDER WITH A FRACTIONAL DERIVATIVE AND WITH A BESSEL OPERATOR
DOI:
https://doi.org/10.52754/16948645_2024_1(4)_45Keywords:
pseudoparabolic equation, boundary value problems, fractional order differential equation, Caputo fractional derivative, Riemann-Liouville fractional integral, Fourier method, Mittag-Leffler functionAbstract
At present, in connection with the problems of heat transfer in a heterogeneous environment, moisture transfer in soil, nonstationary filtration process in a fractured-porous medium, and a number of other problems, interest in the study of initial-boundary value and boundary value problems for non-classical partial differential equations has increased significantly. Such non-classical equations include equations of pseudoparabolic type.
In a rectangular domain, the second initial-boundary value problem for a homogeneous third-order pseudoparabolic equation with a time-fractional Caputo derivative and a Bessel operator with respect to another variable is studied. Conditions for the unique solvability of the problem considered in the class of continuously differentiable functions are established. The existence of a solution to the second boundary value problem is proved by the Fourier method.
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