Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

Elshenhab, Ahmed M.; Wang, Xingtao; Mofarreh, Fatemah; Bazighifan, Omar

doi:10.32604/cmes.2022.021512

Cited by 5 publications

(4 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Actually, it is efficient and easy to implement when compared to other analytical methods. Some frequent results in this regards are cited here as [65][66][67]. In this work, we further compare our results with those obtained by the homotopy perturbation method (HPM) by using the Caputo derivative.…”

Section: Introductionmentioning

confidence: 74%

On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

Shah¹,

Abdeljawad²,

Jarad³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

This article studies a nonlinear fractional order Lotka-Volterra prey-predator type dynamical system. For the proposed study, we consider the model under the conformable fractional order derivative (CFOD). We investigate the mentioned dynamical system for the existence and uniqueness of at least one solution. Indeed, Schauder and Banach fixed point theorems are utilized to prove our claim. Further, an algorithm for the approximate analytical solution to the proposed problem has been established. In this regard, the conformable fractional differential transform (CFDT) technique is used to compute the required results in the form of a series. Using Matlab-16, we simulate the series solution to illustrate our results graphically. Finally, a comparison of our solution to that obtained for the Caputo fractional order derivative via the perturbation method is given.

show abstract

Section: Introductionmentioning

confidence: 74%

On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

Shah¹,

Abdeljawad²,

Jarad³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

View full text Add to dashboard Cite

show abstract

“…Thereafter, the authors of [14] explored the FTS of a differential system with impulsive conditions by utilizing a delayed form of exponential function. Some recent noteworthy work on the FTS analysis of dynamical systems can be found in [30][31][32][33][34][35][36][37].…”

Section: Introductionmentioning

confidence: 99%

Finite-Interval Stability Analysis of Impulsive Fractional-Delay Dynamical System

2023

View full text Add to dashboard Cite

Stability analysis over a finite time interval is a well-formulated technique to study the dynamical behaviour of a system. This article provides a novel analysis on the finite-time stability of a fractional-order system using the approach of the delayed-type matrix Mittag-Leffler function. At first, we discuss the solution’s existence and uniqueness for our considered fractional model. Then standard form of integral inequality of Gronwall’s type is used along with the application of the delayed Mittag-Leffler argument to derive the sufficient bounds for the stability of the dynamical system. The analysis of the system is extended and studied with impulsive perturbations. Further, we illustrate the numerical simulations of our analytical study using relevant examples.

show abstract

“…Recently, the representation of solutions of time-delay systems has been considered. In particular, the pioneering study [9,10] produced several innovative findings on the representations of solutions of time-delay systems, which were used in the control problems and stability analysis; see, for instance, [11][12][13][14][15][16][17][18][19][20][21] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Controllability and Hyers–Ulam Stability of Fractional Systems with Pure Delay

2022

Self Cite

View full text Add to dashboard Cite

Linear and nonlinear fractional-delay systems are studied. As an application, we derive the controllability and Hyers–Ulam stability results using the representation of solutions of these systems with the help of their delayed Mittag–Leffler matrix functions. We provide some sufficient and necessary conditions for the controllability of linear fractional-delay systems by introducing a fractional delay Gramian matrix. Furthermore, we establish some sufficient conditions of controllability and Hyers–Ulam stability of nonlinear fractional-delay systems by applying Krasnoselskii’s fixed-point theorem. Our results improve, extend, and complement some existing ones. Finally, numerical examples of linear and nonlinear fractional-delay systems are presented to demonstrate the theoretical results.

show abstract

Exact Solutions and Finite Time Stability of Linear Conformable Fractional Systems with Pure Delay

Cited by 5 publications

References 29 publications

On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

On Nonlinear Conformable Fractional Order Dynamical System via Differential Transform Method

Finite-Interval Stability Analysis of Impulsive Fractional-Delay Dynamical System

Controllability and Hyers–Ulam Stability of Fractional Systems with Pure Delay

Contact Info

Product

Resources

About