Summary In this paper, a finite‐time stability results of linear delay fractional‐order systems is investigated based on the generalized Gronwall inequality and Caputo fractional derivative. Sufficient conditions are proposed to system with order. Numerical given compared other published data in literature demonstrate validity theoretical results.

This study delves into the formulation of innovative integral inequalities, specifically designed to accommodate weakly singular singularities, thus significantly broadening scope previously established ones. The methodology employed centers around application weighted fractional differential equations, leading derivation a diverse array practical applications for all contextualized within framework Caputo.

ABSTRACT This paper explores the existence, uniqueness, and averaging principles of neutral fractional stochastic Itô–Doob differential equations (NFSIDDEs). By utilizing Picard iteration technique (PIT), we establish existence uniqueness solutions. Additionally, demonstrate principle for NFSIDDEs through utilization key inequalities, including Gronwall Hölder inequalities. Our findings contribute to a deeper understanding qualitative behavior stability properties NFSIDDEs, incorporating...

This article examines the links between trauma and memory implications for identity in Jessamine Chan's novel, The School Good Mothers. It describes how intergenerational impacts Frida (the protagonist) her interactions with Harriet from respective perspectives of psychoanalytic theory pluralistic models. Based on analysis, Frida's behaviours are significantly shaped by unresolved childhood social expectations related to motherhood. Hence, novel critiques institutional approaches dealing...

Abstract This study describes stability analysis that guarantees a part of the solutions will converge to small ball centered in origin for ‐fractional‐order systems ( ‐FOS). Such nonlinear are explored, and such practical is guaranteed by using Lyapunov‐like functions. delves into theoretical underpinnings stability. Additionally, it clarifies this concept through an application.

ABSTRACT This paper delves into the analysis of observability and controllability within framework time‐invariant linear fractional quantum control systems (LFqCS). Specifically, we explore ‐Gramian matrix LFqCS, investigating its rank criteria, null space, various conditions. Additionally, discuss properties exponential matrix. We establish that is equivalent to having a with full provide theorems concerning an LFqCS. Finally, offer two applications illustrate efficacy our findings.

Abstract In this paper, the problem of a global practical Mittag Leffler feedback stabilization for class nonlinear fractional order systems by means observer is described. The linear matrix inequality approach used to guarantee stability proposed system. An illustrative example given show applicability results.

Abstract The observer design problem for integer‐order systems has been the subject of several studies. However, much less interest given to more general fractional‐order systems, where derivative is between 0 and 1. In this paper, a particular form observers Lipschitz, one‐sided Lipschitz quasi‐one‐sided extended calculus. Then, obtained states estimates are used an eventual feedback control, separation principle tackled. effectiveness proposed scheme shown through simulation two numerical examples.

Abstract In this paper, a finite‐time stability procedure is suggested for class of Caputo‐Katugampola fractional‐order time delay systems. Sufficient conditions are derived to prove fact. Numerical results provided demonstrate the validity our theoretical results.

Abstract The issue of estimating states for classical integer‐order nonlinear systems has been widely addressed in the literature. Yet, generalization existing results to fractional‐order framework represents a fertile area research. Note that, recently, new and advantageous type fractional derivative, conformable was defined. So far, general query designing observers not investigated. In addition, it proved literature that some important tools stability analysis are valid using derivative...

In this research study, the generalized differential transform scheme has been applied to simulate impulsive equations with noninteger order. One specific tool of implemented is that it converts problems into a recurrence equation finally leads easily solution considered problem. The validity and reliability method have successfully accomplished by applying some equations. It shown very suitable efficient for solving classes fractional-order initial value might find wide applications.

This work deals with a new finite time stability (FTS) of neutral fractional order systems delay (NFOTSs). In light this, FTSs NFOTSs are demonstrated in the literature using Gronwall inequality. The innovative aspect our proposed study is application fixed point theory to show FTS NFOTSs. Finally, two examples, theoretical contributions confirmed and substantiated.

In this paper, we investigate the existence and uniqueness theorem (EUT) of Pantograph fractional stochastic differential equations (PFSDE) using Banach fixed point (BFPT). We show Ulam–Hyers stability (UHS) PFSDE by generalized Gronwall inequalities (GGI). illustrate our results two examples.