Second boundary-value problem for the generalized Aller–Lykov equation

Abstract

The equations that describe a new type of wave motion arise in the course of mathematical modeling for continuous media with memory. This refers to differential equations of fractional order, which form the basis for most mathematical models describing a wide class of physical and chemical processes in media with fractal geometry. The paper presents a qualitatively new equation of moisture transfer, which is a generalization of the AllerLykov equation, by introducing the concept of the fractal rate of change in humidity clarifying the presence of flows affecting the potential of humidity. We have studied the second boundary value problem for the AllerLykov equation with the fractional RiemannLiouville derivative. The existence of a solution to the problem has been proved by the Fourier method. To prove the uniqueness of the solution we have obtained an a priori estimate, in terms of a fractional RiemannLiouville using the energy inequality method.

Keywords

• second boundary-value problem
• aller–lykov equation
• fourier method
• fractional riemann–liouville operator of fractional integro-differentiation
• method of energy inequalities