Extended Mittag--Leffler Stability Results for Fuzzy Fractional Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912590060322816 |
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| author | En-naoui, Es-said |
| author_facet | En-naoui, Es-said |
| contents | We extend Lyapunov--type Mittag--Leffler stability analysis for fuzzy nonlinear fractional differential equations (Caputo sense) and introduce a family of stronger, broadly applicable stability results. In particular, we develop (i) uniform Mittag--Leffler stability for variable-order Caputo derivatives, (ii) input-to-state stability (ISS) in the Mittag--Leffler sense and explicit robustness/ultimate bound estimates, (iii) a converse Mittag--Leffler Lyapunov theorem, (iv) a fractional LaSalle invariance principle adapted to the fuzzy setting, and (v) practical and computational criteria including Lyapunov--Krasovskii functionals for delay systems and levelwise LMI tests for linearized models. The paper presents precise assumptions, proof sketches, and preparatory lemmas in the preliminaries; subsequent sections (Step 2 onward) provide rigorous proofs and illustrative examples. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_13350 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Extended Mittag--Leffler Stability Results for Fuzzy Fractional Systems En-naoui, Es-said General Mathematics 34A08 (Primary), 34D20, 34D23, 93D09, 93C42 G.1.0; G.1.6; I.2.3 We extend Lyapunov--type Mittag--Leffler stability analysis for fuzzy nonlinear fractional differential equations (Caputo sense) and introduce a family of stronger, broadly applicable stability results. In particular, we develop (i) uniform Mittag--Leffler stability for variable-order Caputo derivatives, (ii) input-to-state stability (ISS) in the Mittag--Leffler sense and explicit robustness/ultimate bound estimates, (iii) a converse Mittag--Leffler Lyapunov theorem, (iv) a fractional LaSalle invariance principle adapted to the fuzzy setting, and (v) practical and computational criteria including Lyapunov--Krasovskii functionals for delay systems and levelwise LMI tests for linearized models. The paper presents precise assumptions, proof sketches, and preparatory lemmas in the preliminaries; subsequent sections (Step 2 onward) provide rigorous proofs and illustrative examples. |
| title | Extended Mittag--Leffler Stability Results for Fuzzy Fractional Systems |
| topic | General Mathematics 34A08 (Primary), 34D20, 34D23, 93D09, 93C42 G.1.0; G.1.6; I.2.3 |
| url | https://arxiv.org/abs/2509.13350 |