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

Abstract:

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.

Año de publicación:

2020

Keywords:

• Matrix representation of Clifford algebras
• Fractional Cauchy–Riemann operator
• Fractional monogenic functions
• Dirichlet boundary value problem

Fuente:

google

scopus