This article is cited in 3 papers

A problem with generalized fractional integro-differentiation operator of an arbitrary order

O. A. Repin^a, S. K. Kumykova<sup>b

a</sup> Chair of Mathematical Statistics and Econometrics, Samara State Economic University, Samara, Russia
^b Chair of Function Theory and Functional Analysis, Kabardino-Balkarian State University, Nalchik, Russia

Abstract: 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.

UDC: 517.946

Received: 17.10.2011

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2012, 56:12, 50–60

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