Geodesic
Nonlocal problem for partial differential equations of fractional order
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 1, pp. 78-86

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A nonlocal problem is investigated for the partial differential equation (diffusion equation of fractional order) in a finite domain. The boundary condition contains a linear combination of generalized operators of fractional integro-differentiation used on the solution in the characteristics and the solution and its derivative in the degenerating line. The uniqueness of the solution is proved by a modified Tricomi method. The existence of the solution is equivalently reduced to the question of the solvability of Fredholm integral equations of the second kind.
Keywords: operator of fractional integro-differentiation, boundary value problem, Fredholm integral equation of the second kind. 
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     author = {O. A. Repin and A. V. Tarasenko},
     title = {Nonlocal problem for partial differential equations of fractional order},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {78--86},
     publisher = {mathdoc},
     volume = {19},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2015_19_1_a4/}
}
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O. A. Repin; A. V. Tarasenko. Nonlocal problem for partial differential equations of fractional order. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 1, pp. 78-86. http://geodesic.mathdoc.fr/item/VSGTU_2015_19_1_a4/