Mohamed Dilmi, Mourad Dilmi

Existence, Uniqueness and Asymptotic Analysis for a Boundary Value Problem with Riemann-Liouville Fractional Derivative

abstract:
In this paper, we investigate the existence, uniqueness and asymptotic analysis for solutions of a boundary value problem involving the Riemann-Liouville fractional time-derivative of order $\alpha \in\,]1,\frac{3}{2}[$ within an open, bounded domain $Q\subset\mathbb{R}^{r}$ $(r=2$ or $3)$. We apply the Faedo-Galerkin method to prove the existence and uniqueness of solutions to the given problem. An asymptotic behavior of the solution to the problem posed in a thin domain is also presented.

Mathematics Subject Classification: 35R11, 35R35, 78M35

Key words and phrases: Asymptotic analysis, Faedo-Galerkin method, fractional calculus, Riemann-Liouville derivative