This article is cited in 7 papers

On a problem for mixed-type equation with fractional derivative

O. A. Repin

Samara State Economic University, 141 Sovetskoi Armii str., Samara, 443090 Russia

Abstract: 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.

UDC: 517.956

Received: 18.05.2017

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2018, 62:8, 38–42

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