Uncertain Asymptotic Stability Analysis of a Fractional-Order System with Numerical Aspects

Safoura Rezaei Aderyani, Reza Saadati (), Donal O’Regan and Fehaid Salem Alshammari
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Safoura Rezaei Aderyani: School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran
Reza Saadati: School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 13114-16846, Iran
Donal O’Regan: School of Mathematical and Statistical Sciences, University of Galway, University Road, H91 TK33 Galway, Ireland
Fehaid Salem Alshammari: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia

Mathematics, 2024, vol. 12, issue 6, 1-31

Abstract: We apply known special functions from the literature (and these include the Fox H – function, the exponential function, the Mittag-Leffler function, the Gauss Hypergeometric function, the Wright function, the G – function, the Fox–Wright function and the Meijer G – function) and fuzzy sets and distributions to construct a new class of control functions to consider a novel notion of stability to a fractional-order system and the qualified approximation of its solution. This new concept of stability facilitates the obtention of diverse approximations based on the various special functions that are initially chosen and also allows us to investigate maximal stability, so, as a result, enables us to obtain an optimal solution. In particular, in this paper, we use different tools and methods like the Gronwall inequality, the Laplace transform, the approximations of the Mittag-Leffler functions, delayed trigonometric matrices, the alternative fixed point method, and the variation of constants method to establish our results and theory.

Keywords: stability results; special aggregate maps; numerical method (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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