Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Author: search.filters.author.Baleanu, D.Subject: search.filters.subject.Stability

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Now showing 1 - 7 of 7
  • Article
    Citation - WoS: 60
    Citation - Scopus: 68
    Lyapunov-Krasovskii Stability Theorem for Fractional Systems With Delay
    (Editura Acad Romane, 2011) Baleanu, Dumitru; Baleanu, D.; Ranjbar N, A.; Abdeljawad, Thabet; Sadati R, S. J.; Delavari, R. H.; Abdeljawad (Maraaba), T.; Gejji, V.; Matematik
    Fractional calculus techniques and methods started to be applied during the last decades in several fields of science and engineering. In this paper we studied the stability of fractional order nonlinear time-delay systems for Caputo's derivative and we extended Lyapunov-Krasovskii theorem for the fractional nonlinear systems.
  • Article
    Hyers-Ulam Stability of Fractional Stochastic Differential Equations With Random Impulse
    (Comenius Univ, 2022) Varshini, S.; Banupriya, K.; Ramkumar, K.; Ravikumar, K.; Baleanu, D.; Kandasamy, Banupriya; Sandrasekaran, Varshini; Kasinathan, Ramkumar
    The goal of this study is to derive a class of random impulsive fractional stochastic differential equations with finite delay that are of Caputo-type. Through certain constraints, the existence of the mild solution of the aforementioned system are acquired by Kransnoselskii's fixed point theorem. Furthermore, through Ito isometry and Gronwall's inequality, the Hyers-Ulam stability of the reckoned system is evaluated using Lipschitz condition.
  • Article
    Citation - WoS: 50
    Citation - Scopus: 55
    Numerical Analysis of Atangana-Baleanu Fractional Model To Understand the Propagation of a Novel Corona Virus Pandemic
    (Elsevier, 2022) Butt, A. I. K.; Ahmad, W.; Rafiq, M.; Baleanu, D.
    In this manuscript, we formulated a new nonlinear SEIQR fractional order pandemic model for the Corona virus disease (COVID-19) with Atangana-Baleanu derivative. Two main equilibrium points F-0*, F-1* of the proposed model are stated. Threshold parameter R-0 for the model using next generation technique is computed to investigate the future dynamics of the disease. The existence and uniqueness of solution is proved using a fixed point theorem. For the numerical solution of fractional model, we implemented a newly proposed Toufik-Atangana numerical scheme to validate the importance of arbitrary order derivative q and our obtained theoretical results. It is worth mentioning that fractional order derivative provides much deeper information about the complex dynamics of Corona model. Results obtained through the proposed scheme are dynamically consistent and good in agreement with the analytical results. To draw our conclusions, we explore a complete quantitative analysis of the given model for different quarantine levels. It is claimed through numerical simulations that pandemic could be eradicated faster if a human community selfishly adopts mandatory quarantine measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effectiveness of quarantine policy on human population. (c) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/ 4.0/).
  • Conference Object
    Citation - Scopus: 1
    Modeling and Analysis of Smokers Model With Constant Proportional Fractional Operators
    (Institute of Electrical and Electronics Engineers Inc., 2023) Baleanu, D.; Farman, M.
    Despite the existence of a secure environment, smoke subjection continues to be a leading cause of serious illness globally. For investigation and observation of the dynamical transmission of the smoker, we examine a fractional order smoker model with Constant Proportional Atangana-Baleanu (in Caputo sense) operator. We treated the proposed model's positivity, boundedness, well-posedness and stability analysis of the model. There is a brief discussion of additional analysis on CPABC operators. Using the Laplace Adomian Decomposition Method, we simulate a system of fractional differential equations numerically. This model's tools seem to be quite strong and capable of reproducing the issue's anticipated theoretical conditions. © 2023 IEEE.
  • Article
    Citation - Scopus: 12
    Stability and Existence Analysis To a Coupled System of Caputo Type Fractional Differential Equations With Erdelyi-Kober Integral Boundary Conditions
    (Natural Sciences Publishing, 2020) Baleanu, D.; Subramanian, M.
    This article focuses on the Hyers-Ulam type stability, existence and uniqueness of solutions for new types of coupled boundary value problems involving fractional differential equations of Caputo type and augmented with Erdelyi-Kober fractional integral boundary conditions. The nonlinearity relies on the unknown functions. The consequence of the existence is obtained through the Leray-Schauder alternative, whereas the uniqueness of the solution relies on the Banach contraction mapping principle.We analyze the stability of the solutions concerned in the Hyers-Ulam form. As an application, some examples are presented to illustrate the main results. Finally, some variants of the problem are addressed. © 2020 NSP Natural Sciences Publishing Cor.
  • Article
    Citation - WoS: 196
    Citation - Scopus: 199
    Impulsive Effects on Stability and Passivity Analysis of Memristor-Based Fractional-Order Competitive Neural Networks
    (Elsevier, 2020) Chanthorn, P.; Niezabitowski, M.; Raja, R.; Baleanu, D.; Pratap, A.; Rajchakit, G.
    This paper analyzes the stability and passivity problems for a class of memristor-based fractional-order competitive neural networks (MBFOCNNs) by using Caputo's fractional derivation. Firstly, impulsive effects are taken well into account and effective analysis techniques are used to reflect the system's practically dynamic behavior. Secondly, by using the Lyapunov technique, some sufficient conditions are obtained by linear matrix inequalities (LMIs) to ensure the stability and passivity of the MBFOCNNs, which can be effectively solved by the LMI computational tool in MATLAB. Finally, two numerical models and their simulation results are given to illustrate the effectiveness of the proposed results. (C) 2020 Elsevier B.V. All rights reserved.
  • Article
    Citation - WoS: 19
    Citation - Scopus: 24
    A Coupled System of Generalized Sturm-Liouville Problems and Langevin Fractional Differential Equations in the Framework of Nonlocal and Nonsingular Derivatives
    (Springer, 2020) Alzabut, J.; Jonnalagadda, J. M.; Adjabi, Y.; Matar, M. M.; Baleanu, D.
    In this paper, we study a coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations described by Atangana-Baleanu-Caputo (ABC for short) derivatives whose formulations are based on the notable Mittag-Leffler kernel. Prior to the main results, the equivalence of the coupled system to a nonlinear system of integral equations is proved. Once that has been done, we show in detail the existence-uniqueness and Ulam stability by the aid of fixed point theorems. Further, the continuous dependence of the solutions is extensively discussed. Some examples are given to illustrate the obtained results.