Solvability and Volterra property of nonlocal problems for mixed fractional-order diffusion-wave equation

Abstract

Abstract The paper is devoted to the study of one class of problems with nonlocal conditions for a mixed diffusion-wave equation with two independent variables. The main results of the work are the proof of regular and strong solvability, as well as the Volterra property of three problems with conditions pointwise connecting the values of the tangent derivative of the desired solution on one of the characteristics with derivatives in various directions of the solution on an arbitrary curve lying inside the characteristic triangle for a fractional-order diffusion-hyperbolic equation.

Keywords

• Diffusion-wave equation
• Nonlocal conditions
• Solvability
• Volterra property
• Fractional-order operator