Existence, uniqueness and asymptotic analysis for a boundary value problem with Riemann–Liouville fractional derivative

Abstract

This thesis investigates a boundary value problem involving the Riemann-Liouville fractional derivative in time of order a €(1, 3/2). By employing tools from functional analysis together with the Faedo-Galerkin method, we establish the existence and uniqueness of a weak solution.

We then analyze the asymptotic behavior of this solution when the problem is formulated in a thin two-dimensional domain, as the thickness parameter (2) tends to zero. Following an appropriate rescaling, we derive uniform a priori estimates independent of (c) and rigorously obtain a reduced limit problem