Geodesic
A problem with generalized fractional integro-differentiation operator of an arbitrary order
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 59-71

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For a degenerate hyperbolic equation we study a problem with fractional integro-differentiation operators in the boundary condition on the characteristic part of the boundary. We determine intervals of variation of parameters of generalized operators of an arbitrary order with the Gauss hypergeometric function with which the problem is either uniquely solvable or has more than one solution.
Keywords: Riemann–Liouville integral and derivative of a fractional order, Volterra and Abel integral equations, Gauss hypergeometric function, resolvent of the kernel. 
@article{IVM_2012_12_a5,
     author = {O. A. Repin and S. K. Kumykova},
     title = {A problem with generalized fractional integro-differentiation operator of an arbitrary order},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {59--71},
     publisher = {mathdoc},
     number = {12},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_12_a5/}
}
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O. A. Repin; S. K. Kumykova. A problem with generalized fractional integro-differentiation operator of an arbitrary order. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2012), pp. 59-71. http://geodesic.mathdoc.fr/item/IVM_2012_12_a5/