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

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