Center Manifold Reduction for Caputo–Hadamard Fractional Differential System

Abstract The aim of this paper is to establish a local fractional center manifold reduction that aligns with the distinctive characteristics of Caputo–Hadamard fractional differential system (C-HFDS). First, based on the theory of local invariant manifold, an adequate notion of local Hadamard fractional center manifold with respect to δ-derivative for C-HFDS is proposed. Then, the existence and approximation of such Hadamard fractional center manifold are demonstrated and realized through the application of a suitable Gronwall inequality with a weakly singular kernel and the Banach contraction principle. Finally, the stability of the Hadamard fractional center manifold is also observed and analyzed on account of the estimation of matrix Mittag-Leffler function and Beesack inequality involved. Not only that, all illustrations are provided to substantiate the validity and efficiency of theoretical findings as well.