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Safoura Hashemishahraki

Publications and source records attributed to Safoura Hashemishahraki.

5 recordsLinked to original sources
arXiv2026

A Stability Testing Algorithm for Incommensurate Fractional Differential Equation Systems

We consider the question of determining whether or not a given system of fractional-order differential equations is (asymptotically) stable. In particular, we admit systems where each constituent equation may have its own order, independent of the order of the other equations in the system, i.e. we discuss the so-called incommensurate case. Exploiting ideas based in numerical linear algebra, we present an algorithm that can be used to answer this question that is much simpler than known methods. We discuss in detail the case of linear problems where the ratios of orders are rational and indicate how known techniques can be used to apply our findings also to general nonlinear problems with arbitrary orders. A MATLAB implementation of the code is provided.

math.DS↗
arXiv2026

Hill-Type Stability Analysis of Periodic Solutions of Fractional-Order Differential Equations

This paper explores stability properties of periodic solutions of (nonlinear) fractional-order differential equations (FODEs). As classical Caputo-type FODEs do not admit exactly periodic solutions, we propose a framework of Liouville-Weyl-type FODEs, which do admit exactly periodic solutions and are an extension of Caputo-type FODEs. Local linearization around a periodic solution results in perturbation dynamics governed by a linear time-periodic differential equation. In the classical integer-order case, the perturbation dynamics is therefore described by Floquet theory, i.e. the exponential growth or decay of perturbations is expressed by Floquet exponents which can be assessed using the Hill matrix approach. For fractional-order systems, however, a rigorous Floquet theory is lacking. Here, we explore the limitations when trying to extend Floquet theory and the Hill matrix method to linear time-periodic fractional-order differential equations (LTP-FODEs) as local linearization of nonlinear fractional-order systems. A key result of the paper is that such an extended Floquet theory can only assess exponentially growing solutions of LTP-FODEs. Moreover, we provide an analysis of linear time-invariant fractional-order systems (LTI-FODEs) with algebraically decaying solutions and show that the inaccessibility of decaying solutions through Floquet theory is already present in the time-invariant case.

eess.SY↗
arXiv2024

On the separation of solutions to fractional differential equations of order $α\in (1,2)$

Given the Caputo-type fractional differential equation $D^αy(t) = f(t, y(t))$ with $α\in (1, 2)$, we consider two distinct solutions $y_1, y_2 \in C[0,T]$ to this equation subject to different sets of initial conditions. In this framework, we discuss nontrivial upper and lower bounds for the difference $|y_1(t) - y_2(t)|$ for $t \in [0,T]$. The main emphasis is on describing how such bounds are related to the differences of the associated initial values.

math.CA↗
arXiv2024

A constructive approach for investigating the stability of incommensurate fractional differential systems

This paper is devoted to studying the asymptotic behaviour of solutions to generalized non-commensurate fractional systems. To this end, we first consider fractional systems with rational orders and introduce a criterion that is necessary and sufficient to ensure the stability of such systems. Next, from the fractional-order pseudospectrum definition proposed by Šanca et al., we formulate the concept of a rational approximation for the fractional spectrum of a noncommensurate fractional systems with general, not necessarily rational, orders. Our first important new contribution is to show the equivalence between the fractional spectrum of a noncommensurate linear system and its rational approximation. With this result in hand, we use ideas developed in our earlier work to demonstrate the stability of an equilibrium point to nonlinear systems in arbitrary finite-dimensional spaces. A second novel aspect of our work is the fact that the approach is constructive. Finally, we give numerical simulations to illustrate the merit of the proposed theoretical results.

math.NA↗