A Dirichlet Boundary Value Problem for Fractional Monogenic Functions in the Riemann–Liouville Sense

This paper solves the Dirichlet boundary value problem of distinguishing domains for Clifford fractional–monogenic functions in Rⁿ for fixed n, in the Riemann–Liouville sense. To do so, we use a matrix representation of the Clifford algebras. This allows us to construct computational algorithms that efficiently perform the calculations necessary to guarantee the existence of a solution for the Dirichlet boundary value problem over a properly distinguished domain. Finally, we show some explicit solutions for the Dirichlet boundary problem in R³.