Browsing by Author "Jajarmi, A."

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Citation - Scopus: 1
A Fractional Lagrangian Approach for Two Masses with Linear and Cubic Nonlinear Stiffness
(Institute of Electrical and Electronics Engineers Inc., 2023) Defterli, O.; Baleanu, D.; Jajarmi, A.; Wannan, R.; Asad, J.; 31401; 56389; Matematik
In this manuscript, the fractional dynamics of the two-mass spring system with two kinds of stiffness, namely linear and strongly nonlinear, are investigated. The corresponding fractional Euler-Lagrange equations of the system are derived being a system of two-coupled fractional differential equations with strong cubic nonlinear term. The numerical results of the system are obtained using Euler's approximation method and simulated with respect to the different values of the model parameters as mass, stiffness and order of the fractional derivative in use. The interpretation of the approximate results of the so-called generalized two-mass spring system is discussed via the fractional order. © 2023 IEEE.
Citation - Scopus: 0
A General Form of Fractional Derivatives for Modelling Purposes in Practice
(Institute of Electrical and Electronics Engineers Inc., 2023) Jajarmi, A.; Baleanu, D.; 56389; Matematik
In this paper, we propose new mathematical models for the complex dynamics of the world population growth as well as a human body's blood ethanol concentration by using a general formulation in fractional calculus. In these new models, we employ a recently introduced ψ-Caputo fractional derivative whose kernel is defined based on another function. Meanwhile, a number of comparative experiences are carried out in order to verify the models according to some sets of real data. Simulation results indicate that better approximations are achieved when the systems are modeled by using the new general fractional formulation than the other cases of fractional- and integer-order descriptions. © 2023 IEEE.
Citation - WoS: 108
Citation - Scopus: 120
A hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems
(Sage Publications Ltd, 2018) Mohammadi, F.; Moradi, L.; Baleanu, D.; Jajarmi, A.; 56389; Matematik
In this paper, a numerical scheme based on hybrid Chelyshkov functions (HCFs) is presented to solve a class of fractional optimal control problems (FOCPs). To this end, by using the orthogonal Chelyshkov polynomials, the HCFs are constructed and a general formulation for their operational matrix of the fractional integration, in the Riemann-Liouville sense, is derived. This operational matrix together with HCFs are used to reduce the FOCP to a system of algebraic equations, which can be solved by any standard iterative algorithm. Moreover, the application of presented method to the problems with a nonanalytic dynamic system is investigated. Numerical results confirm that the proposed HCFs method can achieve spectral accuracy to approximate the solution of FOCPs.
Citation - WoS: 89
Citation - Scopus: 108
A new and general fractional Lagrangian approach: A capacitor microphone case
(Elsevier, 2021) Jajarmi, A.; Baleanu, D.; Vahid, K. Zarghami; Pirouz, H. Mohammadi; Asad, J. H.; 56389; Matematik
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.
Citation - WoS: 140
Citation - Scopus: 168
A new comparative study on the general fractional model of COVID-19 with isolation and quarantine effects
(Elsevier, 2022) Baleanu, D.; Abadi, M. Hassan; Jajarmi, A.; Vahid, K. Zarghami; Nieto, J. J.; 56389; Matematik
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 - WoS: 270
Citation - Scopus: 292
A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
(Amer inst Physics, 2019) Baleanu, D.; Jajarmi, A.; Sajjadi, S. S.; Mozyrska, D.; 56389; Matematik
In this paper, we present a new fractional-order mathematical model for a tumor-immune surveillance mechanism. We analyze the interactions between various tumor cell populations and immune system via a system of fractional differential equations (FDEs). An efficient numerical procedure is suggested to solve these FDEs by considering singular and nonsingular derivative operators. An optimal control strategy for investigating the effect of chemotherapy treatment on the proposed fractional model is also provided. Simulation results show that the new presented model based on the fractional operator with Mittag-Leffler kernel represents various asymptomatic behaviors that tracks the real data more accurately than the other fractional- and integer-order models. Numerical simulations also verify the efficiency of the proposed optimal control strategy and show that the growth of the naive tumor cell population is successfully declined. Published under license by AIP Publishing.
Citation - WoS: 95
Citation - Scopus: 115
A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system
(Springer Science and Business Media Deutschland GmbH, 2021) Baleanu, D.; Zibaei, S.; Namjoo, M.; Jajarmi, A.; 56389; Matematik
The aim of this paper is to introduce and analyze a novel fractional chaotic system including quadratic and cubic nonlinearities. We take into account the Caputo derivative for the fractional model and study the stability of the equilibrium points by the fractional Routh–Hurwitz criteria. We also utilize an efficient nonstandard finite difference (NSFD) scheme to implement the new model and investigate its chaotic behavior in both time-domain and phase-plane. According to the obtained results, we find that the new model portrays both chaotic and nonchaotic behaviors for different values of the fractional order, so that the lowest order in which the system remains chaotic is found via the numerical simulations. Afterward, a nonidentical synchronization is applied between the presented model and the fractional Volta equations using an active control technique. The numerical simulations of the master, the slave, and the error dynamics using the NSFD scheme are plotted showing that the synchronization is achieved properly, an outcome which confirms the effectiveness of the proposed active control strategy. © 2021, The Author(s).
Citation - WoS: 66
Citation - Scopus: 69
Classical and Fractional Aspects of Two Coupled Pendulums
(Editura Acad Romane, 2019) Baleanu, D.; Jajarmi, A.; Asad, J. H.; 56389; Matematik
In this study, we consider two coupled pendulums (attached together with a spring) having the same length while the same masses are attached at their ends. After setting the system in motion we construct the classical Lagrangian, and as a result, we obtain the classical Euler-Lagrange equation. Then, we generalize the classical Lagrangian in order to derive the fractional Euler-Lagrange equation in the sense of two different fractional operators. Finally, we provide the numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on the Euler method to discretize the convolution integral. Numerical simulations show that the proposed approach is efficient and demonstrate new aspects of the real-world phenomena.
Citation - WoS: 60
Citation - Scopus: 66
Dynamical behaviours and stability analysis of a generalized fractional model with a real case study
(Elsevier, 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 oppor-tunities 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, diag-nosed, 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 beha-viours 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 com-pared 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.& COPY; 2023 The Authors. Published by Elsevier B.V. on behalf of Cairo University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Citation - WoS: 112
Citation - Scopus: 125
Novel Fractional-Order Lagrangian to Describe Motion of Beam on Nanowire
(Polish Acad Sciences inst Physics, 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.
Citation - WoS: 77
Citation - Scopus: 80
The Motion of a Bead Sliding on a Wire in Fractional Sense
(Polish Acad Sciences inst Physics, 2017) Baleanu, D.; Jajarmi, A.; Asad, J. H.; Blaszczyk, T.; 56389; Matematik
In this study, we consider the motion of a bead sliding on a wire which is bent into a parabola form. We first introduce the classical Lagrangian from the system model under consideration and obtain the classical Euler-Lagrange equation of motion. As the second step, we generalize the classical Lagrangian to the fractional form and derive the fractional Euler-Lagrange equation in terms of the Caputo fractional derivatives. Finally, we provide numerical solution of the latter equation for some fractional orders and initial conditions. The method we used is based on a discretization scheme using a Grunwald-Letnikov approximation for the fractional derivatives. Numerical simulations verify that the proposed approach is efficient and easy to implement.