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

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–...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-08, Vol.47 (12), p.10490-10506
Main Author: Arfaoui, Hassen
Format: Article
Language:English
Subjects:
Caputo fractional derivative
Derivatives
Dimensional analysis
Dimensional stability
Finite difference method
Fourier analysis
Fractional calculus
Hilbert space
Linear systems
numerical simulation
Partial differential equations
Polynomials
stability of fractional systems
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Summary: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.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.10135