We study reparametrization-invariant systems, mainly the relativistic particle and its D-dimensional extended object generalization d-brane. The corresponding matter Lagrangians naturally contain background interactions, like electromagnetism and gravity. For a dbrane that doesn’t alter the background fields, we define non-relativistic equations assuming integral sub-manifold embedding of the d...

In this paper, the fractional partial differential equations are defined by modified Riemann-Liouville fractional derivative. With the help of fractional derivative and fractional complex transform, these equations can be converted into the nonlinear ordinary differential equations. By using solitay wave ansatz method, we find exact analytical solutions of the space-time fractional Zakharov Kuz...