Résumé: In this work, we examine a porous-elastic system with a fractional operator incorporated in the memory term, which acts exclusively on one equation within the system. Under appropriate conditions on the polynomially decreasing kernels of the memory type, we establish the result of polynomial decay.

Résumé: The objective of this paper is to analyse the asymptotic behavior of a Timoshenko beam system with fractional delays and nonlinear external sources. Under suitable conditions on the damping, delay and initial data, we obtain exponential decay rate of the solution.

Résumé: Addiction-advection equation is a partial differential equation which has many applications in industry and searching for accurate numerical methods to solve it is of great importance. In this work, we propose two methods, the finite difference method (FDM) and the finite volume method (FVM). A discretization of the space fractional advection-diffusion model was used in both methods. The fractional derivatives terms are discretized using fractionally shifted Grünwald formulas. We compare the solutions of these two methods for a case study with an exact solution.