Browsing by Author "Mallawi, Fouad"

Now showing 1 - 3 of 3

Citation Count: Ullah, M.Z...et al. (2020). "A New Fractional Study On the Chaotic Vibration and State-Feedback Control of A Nonlinear Suspension System", Chaos, Solitons and Fractals, Vol. 132.
A New Fractional Study On the Chaotic Vibration and State-Feedback Control of A Nonlinear Suspension System
(Elsevier LTD., 2020) Ullah, Malik Zaka; Mallawi, Fouad; Baleanu, Dumitru; Alshomrani, Ali Saleh; 56389
This paper aims to establish a new fractional model to identify the complex behaviors of a magnetorheological suspension system under the road excitation of sinusoidal function. In the new model, we employ a recently introduced fractional operator with Mittag–Leffler kernel. To implement the model, we develop an efficient approximation scheme and discuss its stability and convergence analysis. We identify the complex behaviors by using the analysis of time-domain responses and phase portraits. The results show that the new fractional model has a strong capability to identify different characteristics of the system under investigation, including chaotic and nonchaotic behaviors. Finally, to avoid the chaotic vibration, a state-feedback controller is designed and its efficiency is proved by some simulation experiments.
Citation Count: Baleanu, Dumitru...et al. (2021). "A new generalization of the fractional Euler-Lagrange equation for a vertical mass-spring-damper", Journal of Vibration and Control, Vol. 27, No. 21-22, pp. 2513-2522.
A new generalization of the fractional Euler-Lagrange equation for a vertical mass-spring-damper
(2021) Baleanu, Dumitru; Ullah, Malik Zaka; Mallawi, Fouad; Alshomrani, Ali Saleh; 56389
In this new study, we investigate the motion of a forced mass-spring-damper in a vertical position. First, the classical Lagrangian as well as the classical Euler-Lagrange equation of motion are constructed. Then the fractional Euler-Lagrange equation is derived by extending the classical Lagrangian in the fractional sense. In this extension, a new form of the fractional derivative is employed including a general function as its kernel. The derived fractional Euler-Lagrange equation is then converted into a system of linear algebraic equation by designing an efficient matrix approximation approach. The numerical findings are reported verifying the theoretical investigations. According to the results, some remarkable thinks are achieved; indeed, the numerical simulations show that different aspects of the system under study can be explored with regard to the flexibility found in selecting the kernel contrary to the traditional fractional models.
Citation Count: Bhrawy, A.H., Baleanu, D., Mallawi, F. (2015). A new numerical technique for solving fractional sub-diffusion and reaction sub-diffusion equations with a non-linear source term. Thermal Science, 19, 25-34. http://dx.doi.org/10.2298/TSCI15S1S25B
A new numerical technique for solving fractional sub-diffusion and reaction sub-diffusion equations with a non-linear source term
(Vinca Inst Nuclear Sci., 2015) Bhrawy, Ali H.; Baleanu, Dumitru; Mallawi, Fouad
In this paper, we are concerned with the fractional sub-diffusion equation with a non-linear source term. The Legendre spectral collocation method is introduced together with the operational matrix of fractional derivatives (described in the Caputo sense) to solve the fractional sub-diffusion equation with a non-linear source term. The main characteristic behind this approach is that it reduces such problems to those of solving a system of algebraic equations which greatly simplifying the problem. In addition, the Legendre spectral collocation methods applied also for a solution of the fractional reaction sub-diffusion equation with a non-linear source term. For confirming the validity and accuracy of the numerical scheme proposed, two numerical examples with their approximate solutions are presented with comparisons between our numerical results and those obtained by other methods.