Geodesic
Problem with shift for the third-order equation with discontinuous coefficients
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2012), pp. 17-25

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The unique solvability of boundary value problem with Saigo operators for the third-order equation with multiple characteristics was investigated. The uniqueness theorem with constraints of inequality type on the known functions and different orders of generalized fractional integro-differentiation was proved. The existence of solution is equivalently reduced to the solvability of Fredholm integral equation of the second kind.
Keywords: boundary value problem, Gauss hypergeometric function, operators of fractional order, Fredholm equation. 
@article{VSGTU_2012_4_a1,
     author = {O. A. Repin and S. K. Kumykova},
     title = {Problem with shift for the third-order equation with discontinuous coefficients},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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     publisher = {mathdoc},
     number = {4},
     year = {2012},
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     url = {http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a1/}
}
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O. A. Repin; S. K. Kumykova. Problem with shift for the third-order equation with discontinuous coefficients. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2012), pp. 17-25. http://geodesic.mathdoc.fr/item/VSGTU_2012_4_a1/