Fractional differential equations have become a fundamental modelling approach for understanding and simulating the many aspects of non-locality spatial heterogeneity complex materials systems. Yet, while real-order fractional operators are nowadays widely adopted, little progress has been made in extending such to complex-order counterparts. In this work, we introduce new definitions Laplacian...

We continue our study of contour deformation as a practical tool for dealing with the sign problem using $d$-dimensional Bose gas non-zero chemical potential toy model. derive explicit expressions contours up to second order respect natural small parameter and generalise these an ansatz which evaluation Jacobian is fast ($O(1)$). examine behaviour various proposed function space-time dimensiona...