Weak solutions of fractional differential equations in non cylindrical domains. (August 2017) - Kubica, A.; Rybka, P.; Ryszewska, K.
Abstract: We study a time fractional heat equation in a non cylindrical domain. The problem is one-dimensional. We prove existence of properly defined weak solutions by means of the Galerkin approximation. Highlights: A time fractional diffusion equation in non cylindrical domains is studied. The Galerkin method is used to obtain a weak solution. Special approximate solutions are defined to obtain a priori estimates. A notion of a weak solution is worked out.