Solvability and Mittag–Leffler–Ulam stability for fractional Duffing problem with three sequential fractional derivatives

In this paper, we discuss the existence, uniqueness, and the Mittag–Leffler–Ulam stability of solutions for fractional Duffing equations involving three fractional derivatives. Uniqueness result for solution of the underlying Duffing problem is given with the help of Banach's fixed point theore...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-03, Vol.47 (4), p.1807-1822
Main Authors: Hamid Ganie, Abdul, Houas, Mohamed, AlBaidani, Mashael M.
Format: Article
Language:English
Subjects:
Computation
Duffing equation
existence
Existence theorems
fixed point
Fixed points (mathematics)
Mittag–Leffler–Ulam stability
Stability
Uniqueness
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Summary:In this paper, we discuss the existence, uniqueness, and the Mittag–Leffler–Ulam stability of solutions for fractional Duffing equations involving three fractional derivatives. Uniqueness result for solution of the underlying Duffing problem is given with the help of Banach's fixed point theorem, where the existence result is computed using Leray–Schauder's alternative. Also, the Mittag–Leffler–Ulam stability results are computed by employing generalized singular Gronwall's inequality. An illustrative example is also given.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9719