Polynomial decay of a linear system of PDEs via Caputo fractional‐time derivative

Abstract

An in‐depth study and analysis of the stability of one‐dimensional Linear System of PDEs via Caputo time fractional derivative (LSCFD) was presented. We proved some stability results for the LSCFD in different Hilbert spaces. Indeed, by using Fourier analysis method and the properties of the Mittag–Leffler Function (MLF), some polynomial stability results for LSCFD have been established. Finally, as an application, we used finite difference methods well suited to integer and fractional order derivatives, and performed some numerical experiments to confirm the theoretical results.

Decomposing Method for Space-Time Fractional Order PDEs

“…In contrast, the Riemann -Liouville fractional derivative definition includes specific fractional derivatives (and/or integrals) of the unknown solution at the beginning point x = 0, which are functions of x. The beginning circumstances lack physical characteristics, and the method for measuring these quantities in tests is unclear, making it difficult to allocate them accurately in an analysis [26][27][28][29][30].…”