Boundary value problem for a multidimensional system of equation with Riemann-Liouville derivatives

TL;DR

This paper investigates a boundary-value problem for a multidimensional system of PDEs with Riemann-Liouville fractional derivatives, proving existence and uniqueness, and explicitly constructing solutions using Wright functions.

Contribution

It establishes the existence and uniqueness of solutions for such fractional PDE systems and provides an explicit solution construction method.

Findings

Proved existence and uniqueness of solutions.

Constructed explicit solutions using Wright functions.

Analyzed boundary-value problems with fractional derivatives.

Abstract

In the paper boundary-value problem for a multidimensional system of partial differential equations with fractional derivatives in Riemann-Liouville sense with constant coefficients is studied in a rectangular domain. The existence and uniqueness theorem for the solution of the boundary value problem is proved. The solution is constructed in explicit form in terms of the Wright function of the matrix argument.