Geodesic
Boundary Value Problem with Shift for One Partial Differential Equation Containing Partial Fractional~Derivative
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2014), pp. 22-32

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We investigate a nonlocal boundary value problem for the equation of special type. For $y> 0$ it is the equation of fractional diffusion, which contains partial fractional derivative of Riemann-Liouville. For $y 0$ it is the hyperbolic type equation with two perpendicular lines of degeneracy. The conditions of existence and uniqueness of the solution of the boundary value problem are formulated. The uniqueness of the solution of the problem is proved using the extremum principle and the use of generalized operator of fractional integro-differential in M. Saygo sense. The existence of a solution is reduced to the solvability of differential equations of fractional order, which solution is written out explicitly.
Keywords: boundary value problem, generalized operator of fractional integro-differentiation, Gauss hypergeometric function, Mittag–Leffler function. 
@article{VSGTU_2014_2_a1,
     author = {O. A. Repin},
     title = {Boundary {Value}  {Problem} with {Shift} for {One} {Partial} {Differential} {Equation} {Containing} {Partial} {Fractional~Derivative}},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {22--32},
     publisher = {mathdoc},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2014_2_a1/}
}
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O. A. Repin. Boundary Value  Problem with Shift for One Partial Differential Equation Containing Partial Fractional~Derivative. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2014), pp. 22-32. http://geodesic.mathdoc.fr/item/VSGTU_2014_2_a1/