The equivalence of solutions to fractional and logarithmic Helmholtz equations

A. Biswas, J. Groszkiewicz, P. R. Stinga

We show the following equivalence of solutions to general fractional Helmholtz equations: $u$ is a solution to $$A^{s}u={\lambda }^{s}u$$ for \textit{some} fixed $0<s<2$ and some $\lambda >0$ if and o…