This article is cited in 3 papers

Differential Equations and Mathematical Physics

On nonlocal problem with fractional Riemann–Liouville derivatives for a mixed-type equation

A. V. Tarasenko, I. P. Egorova

Samara State Technical University, Samara, 443100, Russian Federation

Abstract: The unique solvability is investigated for the problem of equation with partial fractional derivative of Riemann–Liouville and boundary condition that contains the generalized operator of fractional integro-differentiation. The uniqueness theorem for the solution of the problem is proved on the basis of the principle of optimality for a nonlocal parabolic equation and the principle of extremum for the operators of fractional differentiation in the sense of Riemann–Liouville. The proof of the existence of solutions is equivalent to the problem of solvability of differential equations of fractional order. The solution is obtained in explicit form.

Keywords: boundary value problem, generalized fractional integro-differentiation operator, Gauss hypergeometric function, fractional differential equation.

UDC: 517.956.6

MSC: 35M12

Received: June 30, 2016
Revised: October 8, 2016
Accepted: December 9, 2016
First online: April 16, 2017

DOI: 10.14498/vsgtu1499

Bibliographic databases:

• 
• 
• 
•