Browsing by Author "Alzabut, J."

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A coupled system of generalized Sturm-Liouville problems and Langevin fractional differential equations in the framework of nonlocal and nonsingular derivatives
(2020) Baleanu, Dumitru; Alzabut, J.; Jonnalagadda, J. M.; Adjabi, Y.; Matar, M. M.; 56389
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.
Nonlinear delay fractional difference equations with applications on discrete fractional lotka–volterra competition model
(2018) Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; 56389
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.
On Hyers–Ulam Mittag-Leffler stability of discrete fractional Duffing equation with application on inverted pendulum
(2020) Baleanu, Dumitru; Baleanu, Dumitru; Alzabut, J.; Vignesh, D.; Abbas, S.; 56389
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.
Oscillation criteria for second order impulsive delay differential equation
(2004) Taş, Kenan; Baleanu, Dumitru; Taş, Kenan; Baleanu, Dumitru; Krupka, D.; Kurpkova, O.; 56389; 4971
A necessary and sufficient condition is obtained for oscillation of bounded solutions of second order impulsive delay differential equations of the form (r(t)x(t))'+p(t)f(x(i(t)))=0, t not equal theta Delta(r(theta(i))x'(theta(i)))+b(i)g(x(sigma(theta(i)))) = 0, i is an element of Z, Deltax(theta(i)) = 0. An example is also inserted to illustrate the effect of impulses on the oscillatory behavior of the solutions.
Robust synchronization of multi-weighted fractional order complex dynamical networks under nonlinear coupling via non-fragile control with leakage and constant delays
(2023) Baleanu, Dumitru; Raja, R.; Dianavinnarasi, J.; Alzabut, J.; Baleanu, Dumitru; 56389
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.