On a class of nonlocal problems for hyperbolic equations with degeneration of type and order

Abstract

Nonlocal problems for the second order hyperbolic model equation were studied in the characteristic area. The type and order of equations degenerate on the same line $y = 0$. Nonlocal condition is given by means of fractional integro-differentiation of arbitrary order on the boundary. Nonlocal condition connects fractional derivatives and integrals of the desired solution. For different values of order operators of fractional integro-differentiation within the boundary condition the unique solvability of the considered problems was proved or non-uniqueness of the solution was estimated.

Keywords

• nonlocal boundary value problem
• fractional integro-differentiation operators
• cauchy problem
• second kind volterra integral equation
• abel integral equation