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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. [ABSTRACT FROM AUTHOR]

In this work, a class of two-dimensional fractional hyperbolic differential linear system (2D-FHDLS) with time delay is investigated. By using generalized Gronwall's inequality, sufficient conditions for the finite time stability (FTS) of two-dimensional fractional hyperbolic differential system with time delay are given. Numerical examples are also given to illustrate the stability result. [ABSTRACT FROM AUTHOR]