Abstract:
This paper presents a qualitatively new equation for moisture transfer referred to the generalized Aller equation. Such generalization facilitate to highlight the specific features of the studied arrays, their structure, physical properties and other processes inherent in the initial equation. We do it introducing the concept for the fractal velocity of change in humidity. The work investigates the Aller type equation for moisture transfer with two Riemann–Liouville fractional operators of different orders. Using the Fourier method, we establish that a solution to the first boundary value problem exists. The energy inequality provides a priori estimate, which leads to the uniqueness of the solution, its stability with respect to the right-hand side and initial data. We obtain solutions for a system of difference equations with constant coefficients arising by the method of lines. In addition, a priori estimates are found that show convergence of solutions to ODE systems with variable fractional coefficients. Numerical experiments are carried out in the efforts to justify the reliability of our theoretical results.
Keywords:pseudo-parabolic equation, Aller equation for moisture transfer, Riemann–Liouville fractional derivative, Fourier method, a priori estimation.
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