Geodesic
Boundary-value problem with Saigo operatos for mixed type equation with fractional derivative
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 81-86

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We set and solve a nonlocal problem for a differential equation, which contains the diffusion equation of fractional order. The boundary condition contains a linear combination of generalized operators with the Gauss hypergeometric function in the kernel. For various values of parameters of these operators we write a solution in explicit form.
Keywords: nonlocal boundary-value problem, generalized operators of fractional integro-differentiation, differential equation of fractional order, Cauchy problem, partial fractional Riemann–Liouville derivative. 
@article{IVM_2018_1_a9,
     author = {O. A. Repin},
     title = {Boundary-value problem with {Saigo} operatos for mixed type equation with fractional derivative},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {81--86},
     publisher = {mathdoc},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_1_a9/}
}
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O. A. Repin. Boundary-value problem with Saigo operatos for mixed type equation with fractional derivative. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 81-86. http://geodesic.mathdoc.fr/item/IVM_2018_1_a9/