Geodesic
On a class of nonlocal problems for hyperbolic equations with degeneration of type and order
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2014), pp. 22-32

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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. 
@article{VSGTU_2014_4_a2,
     author = {O. A. Repin and S. K. Kumykova},
     title = {On a class of nonlocal problems for hyperbolic equations with degeneration of type and order},
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     pages = {22--32},
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O. A. Repin; S. K. Kumykova. On a class of nonlocal problems for hyperbolic equations with degeneration of type and order. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2014), pp. 22-32. http://geodesic.mathdoc.fr/item/VSGTU_2014_4_a2/