Geodesic
On the solvability of nonlocal problem with generalized operators M.~Saigo for Bitsadze--Lykov equation
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2014), pp. 33-41

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A nonlocal boundary value problem for the equation of moisture transfer was studied in the field, which is the union of two characteristic triangles. The novelty of the formulation of the problem lies in the fact that the boundary conditions include operators of generalized of fractional integro-differentiation in the sense of M. Saigo. The uniqueness of the solution of the problem was proved using the extremum principle for hyperbolic equations. Properties of operators of generalized fractional integro-differentiation in the sense of M. Saigo were used in the proof. Existence of a solution is equivalent reduced to the solvability of a characteristic singular integral equation with Cauchy kernel for which the smoothness of the right-hand side was studied.
Keywords: boundary value problem, generalized operator of fractional integro-differentiation, integral equation with Cauchy kernel. 
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     author = {A. V. Tarasenko and I. P. Egorova},
     title = {On the solvability of nonlocal problem with generalized operators {M.~Saigo} for {Bitsadze--Lykov} equation},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {33--41},
     publisher = {mathdoc},
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     year = {2014},
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A. V. Tarasenko; I. P. Egorova. On the solvability of nonlocal problem with generalized operators M.~Saigo for Bitsadze--Lykov equation. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2014), pp. 33-41. http://geodesic.mathdoc.fr/item/VSGTU_2014_4_a3/