Stability for impulsive implicit Hadamard fractional differential equations

Karthikeyan, P.; Arul, Ramasamy

doi:10.26637/mjm0601/0004

Cited by 7 publications

(4 citation statements)

References 22 publications

(16 reference statements)

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“…Also both the existence and the uniqueness and the stability of solutions of fractional differential equations play an important role in the FC. These studies can be found in References 35‐44.…”

Section: Introductionmentioning

confidence: 99%

Iterative learning control for impulsive fractional order time‐delay systems with nonpermutable constant coefficient matrices

Aydın

Mahmudov

2022

Adaptive Control & Signal

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We introduce an impulsive fractional order time-delay systems with nonpermutable constant coefficient matrices whose solution is given by delayed perturbation of Mittag-Leffler type matrix function. The existence and uniqueness of the solution of the system is proved by using Banach contraction principle. The Ulam-Hyers stability of the given system below are demonstrated. Construct the iterative learning control (ILC) problem obtaining from the mentioned system.The conditions of convergence of ILC problem of each of P, D, and D 𝛼 -types are presented and proved. A comprehensive example with three different original reference trajectories is given to illustrate some theoretical results. This article provides novel outcomes.

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Section: Introductionmentioning

confidence: 99%

Iterative learning control for impulsive fractional order time‐delay systems with nonpermutable constant coefficient matrices

Aydın

Mahmudov

2022

Adaptive Control & Signal

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“…Then, we use similar ideas to those used by several researchers in recent studies, involving the existence and uniqueness of solutions of implicit fractional differential equations,. Furthermore, for other examples of implicit fractional differential equations, we suggest [1,2,6,19,29]. Consider the following Hilfer-Hadamard FIDE of the form:…”

Section: An Examplementioning

confidence: 99%

Some existence and stability results of Hilfer-Hadamard fractional implicit differential fractional equation in a weighted space

Palve,

Abdo,

Panchal

2019

Preprint

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This paper studies a nonlinear fractional implicit differential equation (FIDE) with boundary conditions involving a Hilfer-Hadamard type fractional derivative. We establish the equivalence between the Cauchy-type problem (FIDE) and its mixed type integral equation through a variety of tools of some properties of fractional calculus and weighted spaces of continuous functions. The existence and uniqueness of solutions are obtained. Further, the Ulam-Hyers and Ulam-Hyers-Rassias stability are discussed. The arguments in the analysis rely on Schaefer fixed point theorem, Banach contraction principle and generalized Gronwall inequality. At the end, an illustrative example will be introduced to justify our results.

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“…Consequently, fractional‐order differential dynamical systems play a significant role in many real‐life problems like optimal control, financial modeling, cryptography, orbital transfer of satellites, and fluid dynamics. With the current improvements in this theory and applications, we advise the reader to refer to earlier studies [1–21].…”

Section: Introductionmentioning

confidence: 99%

Impulsively fractional‐order time‐delayed gene regulatory networks: Existence and asymptotic stability

Arjunan,

Abdeljawad,

Pratap

et al. 2023

Asian Journal of Control

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This paper presents asymptotic stability criteria for fractional‐order gene regulatory networks (FOGRNs) with impulses, time delays, and two numerical cases to illustrate the applicability of the results. The established system's boundedness, existence, and uniqueness are discussed using the Mittag–Leffler function, homeomorphism theory, and Cauchy–Schwartz inequality. The delay‐independent asymptotic stability criteria for FOGRNs are derived using algebraic and LMI methods, famous inequality techniques, and Lyapunov stability theory.

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Stability for impulsive implicit Hadamard fractional differential equations

Abstract: In this paper, we analyze the uniqueness and stability for implicit fractional differential equations with impulsive conditions involving the hadamard derivative of fractional order α. An illustrative example is also presented.

Cited by 7 publications

References 22 publications

Iterative learning control for impulsive fractional order time‐delay systems with nonpermutable constant coefficient matrices

Iterative learning control for impulsive fractional order time‐delay systems with nonpermutable constant coefficient matrices

Some existence and stability results of Hilfer-Hadamard fractional implicit differential fractional equation in a weighted space

Impulsively fractional‐order time‐delayed gene regulatory networks: Existence and asymptotic stability

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