Geodesic
Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2011), pp. 25-36

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The unique solvability of internally boundary value problem for equation of mixed type of third order with multiple characteristics is investigated. The uniqueness theorem is proved with the restrictions on certain features and different orders of fractional integro-differentiation. The existence of solution is equivalent reduced to a Fredholm integral equation of the second kind.
Keywords: boundary value problem, fractional integro-differentiation operators, Gauss hypergeometric function, Fredholm integral equation. 
@article{VSGTU_2011_4_a3,
     author = {O. A. Repin and S. K. Kumykova},
     title = {Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {25--36},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2011_4_a3/}
}
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O. A. Repin; S. K. Kumykova. Nonlocal problem for a equation of mixed type of third order with generalized operators of fractional integro-differentiation of arbitrary order. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 4 (2011), pp. 25-36. http://geodesic.mathdoc.fr/item/VSGTU_2011_4_a3/