Browsing by Author "Jajarmi, A."

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Citation Count: Jajarmi, A...et al. (2021). "A new and general fractional Lagrangian approach: A capacitor microphone case", Results in Physics, Vol. 31.
A new and general fractional Lagrangian approach: A capacitor microphone case
(2021) Jajarmi, A.; Baleanu, Dumitru; Vahid, K. Zarghami; Pirouz, H. Mohammadi; Asad, J. H.; 56389
In this study, a new and general fractional formulation is presented to investigate the complex behaviors of a capacitor microphone dynamical system. Initially, for both displacement and electrical charge, the classical Euler-Lagrange equations are constructed by using the classical Lagrangian approach. Expanding this classical scheme in a general fractional framework provides the new fractional Euler-Lagrange equations in which non-integer order derivatives involve a general function as their kernel. Applying an appropriate matrix approximation technique changes the latter fractional formulation into a nonlinear algebraic system. Finally, the derived system is solved numerically with a discussion on its dynamical behaviors. According to the obtained results, various features of the capacitor microphone under study are discovered due to the flexibility in choosing the kernel, unlike the previous mathematical formalism.
A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects
(2022) Baleanu, Dumitru; Abadi, M. Hassan; Jajarmi, A.; Vahid, K. Zarghami; Nieto, J. J.; 56389
A generalized version of fractional models is introduced for the COVID-19 pandemic, including the effects of isolation and quarantine. First, the general structure of fractional derivatives and integrals is discussed; then the generalized fractional model is defined from which the stability results are derived. Meanwhile, a set of real clinical observations from China is considered to determine the parameters and compute the basic reproduction number, i.e., R-0 approximate to 6.6361. Additionally, an efficient numerical technique is applied to simulate the new model and provide the associated numerical results. Based on these simulations, some figures and tables are presented, and the data of reported cases from China are compared with the numerical findings in both classical and fractional frameworks. Our comparative study indicates that a particular case of general fractional formula provides a better fit to the real data compared to the other classical and fractional models. There are also some other key parameters to be examined that show the health of society when they come to eliminate the disease. (C) 2021 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University.
Citation Count: Jajarmi, A.; Arshad, S.; Baleanu, Dumitru (2019). "A new fractional modelling and control strategy for the outbreak of dengue fever", Physica A: Statistical Mechanics and its Applications, Vol. 535, No. 1.
A new fractional modelling and control strategy for the outbreak of dengue fever
(2019) Jajarmi, A.; Arshad, S.; Baleanu, Dumitru; 56389
This paper deals with a new mathematical model for a dengue fever outbreak based on a system of fractional differential equations. The equilibrium points and stability of the new system are studied. To simulate this model, a new and efficient numerical method is provided and its stability and convergence are proved. According to a real outbreak on the Cape Verde Islands occurred in year 2009, the new model is examined for a period of three months by using singular or nonsingular kernels in the definition of derivative operator. Simulation results show that the proposed formalism with exponential kernel agrees well with the real data in the early stage of the epidemic while the Mittag-Leffler kernel fits the reality for the later part of the time interval. Hence, the new framework in a hybrid manner can properly simulate the dynamics of the disease in the whole of the time interval. In order to stabilize the disease-free equilibrium point of the system under investigation, two control strategies are suggested. Numerical simulations verify that the proposed stabilizing controllers are efficient and provide significantly remarkable results.
Citation Count: Baleanu, D...et.al. "Dynamical behaviours and stability analysis of a generalized fractional model with a real case study", Journal of Advanced Research, Vol.48, pp.157-173.
Dynamical behaviours and stability analysis of a generalized fractional model with a real case study
(2023) Baleanu, D.; Arshad, S.; Jajarmi, A.; Shokat, W.; Ghassabzade, F. Akhavan; Wali, M.; 56389
Introduction: Mathematical modelling is a rapidly expanding field that offers new and interesting opportunities for both mathematicians and biologists. Concerning COVID-19, this powerful tool may help humans to prevent the spread of this disease, which has affected the livelihood of all people badly. Objectives: The main objective of this research is to explore an efficient mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. Methods: The new model in this paper is formulated in the Caputo sense, employs a nonlinear time-varying transmission rate, and consists of ten population classes including susceptible, infected, diagnosed, ailing, recognized, infected real, threatened, diagnosed recovered, healed, and extinct people. The existence of a unique solution is explored for the new model, and the associated dynamical behaviours are discussed in terms of equilibrium points, invariant region, local and global stability, and basic reproduction number. To implement the proposed model numerically, an efficient approximation scheme is employed by the combination of Laplace transform and a successive substitution approach; besides, the corresponding convergence analysis is also investigated. Results: Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic in Italy. By using these comparisons between the simulated and measured data, we find the best value of the fractional order with minimum absolute and relative errors. Also, the impact of different parameters on the spread of viral infection is analyzed and studied. Conclusion: According to the comparative results with real data, we justify the use of fractional concepts in the mathematical modelling, for the new non-integer formalism simulates the reality more precisely than the classical framework.
Citation Count: Erturk, V. S...et al. (2021). "Novel Fractional-Order Lagrangian to Describe Motion of Beam on Nanowire", ACTA PHYSICA POLONICA A, Vol. 140, No. 3, pp. 265-272.
Novel Fractional-Order Lagrangian to Describe Motion of Beam on Nanowire
(2021) Erturk, V. S.; Godwe, E.; Baleanu, D.; Kumar, P.; Asad, J.; Jajarmi, A.; 56389
Our aim in this research is to investigate the motion of a beam on an internally bent nanowire by using the fractional calculus theory. To this end, we first formulate the classical Lagrangian which is followed by the classical Euler-Lagrange equation. Then, after introducing the generalized fractional Lagrangian, the fractional Euler-Lagrange equation is provided for the motion of the considered beam on the nanowire. An efficient numerical scheme is introduced for implementation and the simulation results are reported for different fractional-order values and various initial settings. These results indicate that the fractional responses approach the classical ones as the fractional order goes to unity. In addition, the fractional Euler-Lagrange equation provides a flexible model possessing more information than the classical description the fact that leads to a considerably better evaluation of the hidden features of the real system under investigation.