Browsing by Author "Alzabut, J."

Now showing 1 - 5 of 5

Citation - WoS: 20
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) Baleanu, D.; Baleanu, Dumitru; Alzabut, J.; Jonnalagadda, J. M.; Adjabi, Y.; Matar, M. M.; 56389; Matematik
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.
Citation - Scopus: 49
Nonlinear delay fractional difference equations with applications on discrete fractional lotka–volterra competition model
(Eudoxus Press, LLC, 2018) Abdeljawad, Thabet; Alzabut, J.; Abdeljawad, T.; Baleanu, Dumitru; Baleanu, D.; 56389; Matematik
The existence and uniqueness of solutions for nonlinear delay fractional difference equations are investigated in this paper. We prove the main results by employing the theorems of Krasnoselskii’s Fixed Point and Arzela–Ascoli. As an application of the main theorem, we provide an existence result on the discrete fractional Lotka–Volterra model. ©2018 by Eudoxus Press, LLC. All rights reserved.
Citation - WoS: 37
Citation - Scopus: 45
On Hyers–Ulam Mittag-Leffler stability of discrete fractional Duffing equation with application on inverted pendulum
(Springer, 2020) Selvam, A. G. M.; Baleanu, Dumitru; Baleanu, D.; Alzabut, J.; Vignesh, D.; Abbas, S.; 56389; Matematik
A human being standing upright with his feet as the pivot is the most popular example of the stabilized inverted pendulum. Achieving stability of the inverted pendulum has become common challenge for engineers. In this paper, we consider an initial value discrete fractional Duffing equation with forcing term. We establish the existence, Hyers-Ulam stability, and Hyers-Ulam Mittag-Leffler stability of solutions for the equation. We consider the inverted pendulum modeled by Duffing equation as an example. The values are tabulated and simulated to show the consistency with theoretical findings.
Citation - WoS: 33
Citation - Scopus: 36
Perron’s theorem for linear impulsive differential equations with distributed delay
(Elsevier Science Bv, 2006) Akhmet, M. U.; Alzabut, Jehad; Alzabut, J.; Zafer, A.; 207728; Matematik
In this paper it is shown that under a Perron condition trivial solution of linear impulsive differential equation with distributed delay is uniformly asymptotically stable. (c) 2005 Elsevier B.V. All rights reserved.
Citation - WoS: 8
Citation - Scopus: 9
Robust synchronization of multi-weighted fractional order complex dynamical networks under nonlinear coupling via non-fragile control with leakage and constant delays
(Pergamon-elsevier Science Ltd, 2023) Aadhithiyan, S.; Baleanu, Dumitru; Raja, R.; Dianavinnarasi, J.; Alzabut, J.; Baleanu, D.; 56389; Matematik
In this article, we examine the impact of leakage delays on robust synchronization for fractional order multi-weighted complex dynamical networks(MFCDN) under non-linear coupling via non-fragile control. By employing the fractional order comparison principle, suitable Lyapunov method, and some fractional order inequality techniques, we ensured the robust asymptotical synchronization for MFCDN. In addition to common findings, we have done some specific research in order to get reliable synchronization for multi-weighted complex dynamical network(MCDN) without leakage delay. Additionally, our findings gained are applicable to single weighted FCDN and integer order complex dynamical networks, regardless of whether they have a single weight or many weights. Our suggested approach is shown to be more effective and practical in this article by providing a numerical simulation.