Geodesic
On a problem for mixed-type equation with fractional derivative
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 46-51

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For a mixed-type equation with a Riemann–Liouville partial fractional derivative we investigate a problem, in which the boundary condition contains a linear combination of generalized fractional operators with a Gauss hypergeometric function. The uniqueness of a solution to the problem is proved for various values of the parameters of these operators. The existence of the solution is presented in an explicit form as a solution to an equation with fractional derivatives of different orders.
Keywords: non-local problem, differential equation of fractional order, generalized operator, Gauss hypergeometric function, Cauchy problem. 
@article{IVM_2018_8_a5,
     author = {O. A. Repin},
     title = {On a problem for mixed-type equation with fractional derivative},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {46--51},
     publisher = {mathdoc},
     number = {8},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_8_a5/}
}
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O. A. Repin. On a problem for mixed-type equation with fractional derivative. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2018), pp. 46-51. http://geodesic.mathdoc.fr/item/IVM_2018_8_a5/