Browsing by Author "Jajarmi, Amin"

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Citation Count: Defterli, Ö.;...et.al. "A Fractional Lagrangian Approach for Two Masses with Linear and Cubic Nonlinear Stiffness", 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023, Proceedings, 2023.
A Fractional Lagrangian Approach for Two Masses with Linear and Cubic Nonlinear Stiffness
(2023) Defterli, Özlem; Balenau, Dumitru; Jajarmi, Amin; Wannan, Rania; Asad, Jihad; 31401; 56389
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.
Citation Count: Jajarmi, A.; Baleanu, D. "A General Form of Fractional Derivatives for Modelling Purposes in Practice", 2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023, Proceedings, 2023.
A General Form of Fractional Derivatives for Modelling Purposes in Practice
(2023) Jajarmi, Amin; Baleanu, Dumitru; 56389
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.
Citation Count: Jajarmi, Amin...et al. (2022). "A general fractional formulation and tracking control for immunogenic tumor dynamics", Mathematical Methods in the Applied Sciences, Vol. 45, No. 2, pp. 667-680.
A general fractional formulation and tracking control for immunogenic tumor dynamics
(2022) Jajarmi, Amin; Baleanu, Dumitru; Vahid, Kianoush Zarghami; Mobayen, Saleh; 56389
Mathematical modeling of biological systems is an important issue having significant effect on human beings. In this direction, the description of immune systems is an attractive topic as a result of its ability to detect and eradicate abnormal cells. Therefore, this manuscript aims to investigate the asymptotic behavior of immunogenic tumor dynamics based on a new fractional model constructed by the concept of general fractional operators. We discuss the stability and equilibrium points corresponding to the new model; then we modify the predictor-corrector method in general sense to implement the model and compare the associated numerical results with some real experimental data. As an achievement, the new model provides a degree of flexibility enabling us to adjust the complex dynamics of biological system under study. Consequently, the new general model and its solution method presented in this paper for the immunogenic tumor dynamics are new and comprise quite different information than the other kinds of classical and fractional equations. In addition to these, we implement a tracking control method in order to decrease the development of tumor-cell population. The satisfaction of control purpose is confirmed by some simulation results since the controlled variables track the tumor-free steady state in the whole realistic cases.
Citation Count: Mohammadi, F.; Moradi, L.; Baleanu, D. "A hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems", Journal of Vibration and Control, Vol. 24, No. 21. pp. 5030-5043, (2018).
A hybrid functions numerical scheme for fractional optimal control problems: Application to nonanalytic dynamic systems
(Sage Publications LTD, 2018) Mohammadi, F.; Moradi, L.; Baleanu, Dumitru; Jajarmi, Amin; 56389
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 Count: Sajjadi, Samaneh Sadat...et al. (2020). "A new adaptive synchronization and hyperchaos control of a biological snap oscillator", Chaos Solitons & Fractals, Vol. 138.
A new adaptive synchronization and hyperchaos control of a biological snap oscillator
(2020) Sajjadi, Samaneh Sadat; Baleanu, Dumitru; Jajarmi, Amin; Pirouz, Hassan Mohammadi; 56389
The purpose of this paper is to analyze and control the hyperchaotic behaviours of a biological snap oscillator. We mainly study the chaos control and synchronization of a hyperchaotic model in both the frameworks of classical and fractional calculus, respectively. First, the phase portraits of the considered model and its hyperchaotic attractors are analyzed. Then two efficacious optimal and adaptive controllers are designed to compensate the undesirable hyperchaotic behaviours. Moreover, applying an efficient adaptive control procedure, we generally synchronize two identical biological snap oscillator models. Finally, a new fractional model is proposed for the considered oscillator in order to acquire the hyperchaotic attractors. Indeed, the fractional calculus leads to more realistic and flexible models with memory effects, which could help us to design more efficient controllers. Considering this feature, we apply a linear state-feedback controller as well as an active control scheme to control hyperchaos and achieve synchronization, respectively. The related theoretical consequences are numerically justified via the obtained simulations and experiments. (C) 2020 Elsevier Ltd. All rights reserved.
Citation Count: Jajarmi, Amin; Ghanbari, Behzad; Baleanu, Dumitru, "A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence", Amer Inst Physics, Vol. 29, No. 9, (2019).
A new and efficient numerical method for the fractional modeling and optimal control of diabetes and tuberculosis co-existence
(Amer Inst Physics, 2019) Jajarmi, Amin; Ghanbari, Behzad; Baleanu, Dumitru; 56389
The main objective of this research is to investigate a new fractional mathematical model involving a nonsingular derivative operator to discuss the clinical implications of diabetes and tuberculosis coexistence. The new model involves two distinct populations, diabetics and nondiabetics, while each of them consists of seven tuberculosis states: susceptible, fast and slow latent, actively tuberculosis infection, recovered, fast latent after reinfection, and drug-resistant. The fractional operator is also considered a recently introduced one with Mittag-Leffler nonsingular kernel. The basic properties of the new model including non-negative and bounded solution, invariant region, and equilibrium points are discussed thoroughly. To solve and simulate the proposed model, a new and efficient numerical method is established based on the product-integration rule. Numerical simulations are presented, and some discussions are given from the mathematical and biological viewpoints. Next, an optimal control problem is defined for the new model by introducing four control variables reducing the number of infected individuals. For the control problem, the necessary and sufficient conditions are derived and numerical simulations are given to verify the theoretical analysis.
Citation Count: Jajarmi, Amin...et al. (2018). "A new approach for the nonlinear fractional optimal control problems with external persistent disturbances",Journal of the Franklin Institute-Engineering and Applied Mathematics, Vol. 355, No. 9, pp. 3938-3967.
A New Approach for the Nonlinear Fractional Optimal Control Problems With External Persistent Disturbances
(Pergamon-Elsevier Science LTD, 2018) Jajarmi, Amin; Hajipour, Mojtaba; Mohammadzadeh, Ehsan; Baleanu, Dumitru; 56389
The aim of this manuscript is to investigate an efficient iterative approach for the nonlinear fractional optimal control problems affected by the external persistent disturbances. For this purpose, first the internal model principle is employed to transform the fractional dynamic system with disturbance into an undisturbed system with both integer- and fractional-order derivatives. The necessary optimality conditions are then reduced into a sequence of linear algebraic equations by using a series expansion approach and the Grunwald-Letnikov approximation for the fractional derivatives. The convergence of the latter sequence to the optimal solution is also studied. In addition, an iterative algorithm designing the suboptimal control law is presented. Numerical simulations confirm that the new approach is efficient to reject the external disturbance and provides satisfactory results compared to the other existing methods. (C) 2018 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.
Citation Count: Jajarmi, Amin; Hajipour, Mojtaba; Baleanu, Dumitru, "A new approach for the optimal control of time-varying delay systems with external persistent matched disturbances", Journal of Vibration And Control, Vol. 24, No. 19, pp. 4505-4512, (2018).
A New Approach for The Optimal Control Of Time-Varying Delay Systems With External Persistent Matched Disturbances
(Sage Publications LTD, 2018) Jajarmi, Amin; Hajipour, Mojtaba; Baleanu, Dumitru; 56389
The aim of this study is to develop an efficient iterative approach for solving a class of time-delay optimal control problems with time-varying delay and external persistent disturbances. By using the internal model principle, the original time-delay model with disturbance is first converted into an augmented system without any disturbance. Then, we select a quadratic performance index for the augmented system to form an undisturbed time-delay optimal control problem. The necessary optimality conditions are then derived in terms of a two-point boundary value problem involving advance and delay arguments. Finally, a fast iterative algorithm is designed for the latter advance-delay boundary value problem. The convergence of the new iterative technique is also investigated. Numerical simulations verify that the proposed approach is efficient and provides satisfactory results.
Citation Count: Jajarmi, A...et al. (2017). "A New Feature of the Fractional Euler–Lagrange Equations for A Coupled Oscillator Using A Nonsingular Operator Approach", Frontiers in Physics, Vol. 7.
A New Feature of the Fractional Euler–Lagrange Equations for A Coupled Oscillator Using A Nonsingular Operator Approach
(Frontiers Media S.A., 2019) Jajarmi, Amin; Baleanu, Dumitru; Sajjadi, S. S.; Asad, Jihad H.; 56389
In this new work, the free motion of a coupled oscillator is investigated. First, a fully description of the system under study is formulated by considering its classical Lagrangian, and as a result, the classical Euler–Lagrange equations of motion are constructed. After this point, we extend the classical Lagrangian in fractional sense, and thus, the fractional Euler–Lagrange equations of motion are derived. In this new formulation, we consider a recently introduced fractional operator with Mittag–Leffler non-singular kernel. We also present an efficient numerical method for solving the latter equations in a proper manner. Due to this new powerful technique, we are able to obtain remarkable physical thinks; indeed, we indicate that the complex behavior of many physical systems is realistically demonstrated via the fractional calculus modeling. Finally, we report our numerical findings to verify the theoretical analysis. © Copyright © 2019 Jajarmi, Baleanu, Sajjadi and Asad.
Citation Count: Baleanu, Dumitru; Jajarmi, Amin; Hajipour, Mojtaba, "A new formulation of the fractional optimal control problems involving mittag-leffler nonsingular kernel", Journal Of Optimization Theory And Applications, Vol.175, No.3, pp.718-737, (2017).
A new formulation of the fractional optimal control problems involving mittag-leffler nonsingular kernel
(Springer/Plenum Publishers, 2017) Baleanu, Dumitru; Jajarmi, Amin; Hajipour, Mojtaba; 56389
The aim of this paper is to propose a new formulation of the fractional optimal control problems involving Mittag-Leffler nonsingular kernel. By using the Lagrange multiplier within the calculus of variations and by applying the fractional integration by parts, the necessary optimality conditions are derived in terms of a nonlinear two-point fractional boundary value problem. Based on the convolution formula and generalized discrete Gronwall's inequality, the numerical scheme for solving this problem is developed and its convergence is proved. Numerical simulations and comparative results show that the suggested technique is efficient and provides satisfactory results.
Citation Count: Jajarmi, Amin; Baleanu, Dumitru, "A new fractional analysis on the interaction of HIV with CD4(+) T-cells", Chaos Solitons & Fractals, Vol. 113, pp. 221-229, (2018)
A New Fractional Analysis On the Interaction of HIV With CD4(+) T-Cells
(Pergamon-Elsevier Science LTD, 2018) Jajarmi, Amin; Baleanu, Dumitru; 56389
Mathematical modeling of biological systems is an interesting research topic that attracted the attention of many researchers. One of the main goals in this area is the design of mathematical models that more accurately illustrate the characteristics of the real-world phenomena. Among the existing research projects, modeling of immune systems has given a growing attention due to its natural capabilities in identifying and destroying abnormal cells. The main objective of this paper is to investigate the pathological behavior of HIV-infection using a new model in fractional calculus. The proposed model is examined through three different operators of fractional derivatives. An efficient numerical method is also presented to solve these fractional models effectively. In fact, we believe that the new models presented on the basis of these three operators show various asymptomatic behaviors that do not appear during the modeling with the integer-order derivatives. Therefore, the fractional calculus provides more precise models of biological systems that help us to make more realistic judgments about their complex dynamics. Finally, simulations results are provided to confirm the theoretical analysis. (C) 2018 Elsevier Ltd. All rights reserved.
Citation Count: Jajarmi, A...et al. (2020). "A New Fractional Hrsv Model and Its Optimal Control: A Non-Singular Operator Approach", Physica A: Statistical Mechanics and Its Applications, Vol. 547.
A New Fractional Hrsv Model and Its Optimal Control: A Non-Singular Operator Approach
(Elsevier B.V., 2020) Jajarmi, Amin; Yusuf, Abdullahi; Baleanu, Dumitru; İnç, Mustafa; 56389
In the current work, a fractional version of SIRS model is extensively investigated for the HRSV disease involving a new derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The fixed-point theory is employed to show the existence and uniqueness of the solution for the model under consideration. In order to see the performance of this model, simulation and comparative analyses are carried out according to the real experimental data from the state of Florida. To believe upon the results obtained, the fractional order is allowed to vary between (0,1) whereupon the physical observations show that the fractional dynamical character depends on the order of derivative operator and approaches an integer solution as α tends to 1. These features make the model more applicable when presented in the structure of fractional-order with ABC derivative. The effect of treatment by an optimal control strategy is also examined on the evolution of susceptible, infectious, and recovered individuals. Simulation results indicate that our fractional modeling and optimal control scheme are less costly and more effective than the proposed approach in the classical version of the model to diminish the HRSV infected individuals.
Citation Count: Baleanu, D...et al. (2019). "A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator", Chaos, Vol. 29, No. 8.
A new fractional model and optimal control of a tumor-immune surveillance with non-singular derivative operator
(Amer Inst Physics, 2019) Baleanu, Dumitru; Jajarmi, Amin; Sajjadi, S. S.; Mozyrska, D.; 56389
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 Count: Baleanu, Dumitru...et.al. (2023). "A new intervention strategy for an HIV/AIDS transmission by a general fractional modeling and an optimal control approach", Chaos Solitons & Fractals, Vol.167.
A new intervention strategy for an HIV/AIDS transmission by a general fractional modeling and an optimal control approach
(2023) Baleanu, Dumitru; Hasanabadi, Manijeh; Vaziri, Asadollah Mahmoudzadeh; Jajarmi, Amin; 56389
This study proposes a new mathematical model in a generalized fractional framework for the investigation of an HIV/AIDS transmission dynamics. An auxiliary parameter further prevents the fractional equations from mismatching in the dimension. In order to analyze the general model, the non-negativity of the solution and the stability of the equilibrium points are examined. The model is also implemented by a powerful numerical scheme based on the quadrature rules and the repeated Trapezoidal method; as well, the error discussion and the convergence analysis are established. In addition, an efficient intervention strategy is developed and examined based on the optimal control theories in terms of optimality necessary conditions. Real-life clinical observations from Cape Verde Islands show that the new fractional model outperforms the classical one with ordinary time-derivatives, and enhances the modeling output compared to the previous fractional mathematical results. Further, numerical simulations demonstrate that the proposed optimal control measure leads to a significant reduction in the disease spread. As a result, the general fractional model offers a degree-of-freedom, an efficient tool which is helpful to illustrate the fundamental features of the disease transmission and to increase the efficiency of the proposed treatment strategy.
Citation Count: Jajarmi, Amin; Baleanu, Dumitru (2020). "A New Iterative Method for the Numerical Solution of High-Order Non-linear Fractional Boundary Value Problems", Frontiers in Physics, Vol. 8.
A New Iterative Method for the Numerical Solution of High-Order Non-linear Fractional Boundary Value Problems
(2020) Jajarmi, Amin; Baleanu, Dumitru; 56389
The boundary value problems (BVPs) have attracted the attention of many scientists from both practical and theoretical points of view, for these problems have remarkable applications in different branches of pure and applied sciences. Due to this important property, this research aims to develop an efficient numerical method for solving a class of non-linear fractional BVPs. The proposed method is free from perturbation, discretization, linearization, or restrictive assumptions, and provides the exact solution in the form of a uniformly convergent series. Moreover, the exact solution is determined by solving only a sequence of linear BVPs of fractional-order. Hence, from practical viewpoint, the suggested technique is efficient and easy to implement. To achieve an approximate solution with enough accuracy, we provide an iterative algorithm that is also computationally efficient. Finally, four illustrative examples are given verifying the superiority of the new technique compared to the other existing results.
Citation Count: Baleanu, D...et al. (2020). "A New Study On the Mathematical Modelling of Human Liver With Caputo–Fabrizio Fractional Derivative", Chaos, Solitons and Fractals, Vol. 134.
A New Study On the Mathematical Modelling of Human Liver With Caputo–Fabrizio Fractional Derivative
(Elsevier LTD., 2020) Baleanu, Dumitru; Jajarmi, Amin; Mohammadi, H.; Rezapour, S.; 56389
In this research, we aim to propose a new fractional model for human liver involving Caputo–Fabrizio derivative with the exponential kernel. Concerning the new model, the existence of a unique solution is explored by using the Picard–Lindelöf approach and the fixed-point theory. In addition, the mathematical model is implemented by the homotopy analysis transform method whose convergence is also investigated. Eventually, numerical experiments are carried out to better illustrate the results. Comparative results with the real clinical data indicate the superiority of the new fractional model over the pre-existent integer-order model with ordinary time-derivatives.
Citation Count: Baleanu, Dumitru...et al. (2021). "A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system", Advances in Difference Equations, Vol. 2021, No. 1.
A nonstandard finite difference scheme for the modeling and nonidentical synchronization of a novel fractional chaotic system
(2021) Baleanu, Dumitru; Zibaei, Sadegh; Namjoo, Mehran; Jajarmi, Amin; 56389
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.
Citation Count: Jajarmi, Amin...et al. (2019). "A robust and accurate disturbance damping control design for nonlinear dynamical systems", Optimal Control Applications & Methods, Vol. 40, no. 3, pp. 375-393.
A robust and accurate disturbance damping control design for nonlinear dynamical systems
(Wiley, 2019) Jajarmi, Amin; Hajipour, Mojtaba; Sajjadi, Samaneh Sadat; Baleanu, Dumitru; 56389
The principle result of this paper is the following disturbance rejection control scheme for a class of nonlinear dynamical systems. By using the internal model principle, the problem of disturbance damping control is converted into a nonlinear quadratic regulator (NQR) problem for an undisturbed augmented system. Then, an iterative technique is designed to solve this NQR problem effectively. The proposed iterative method is also extended through the use of a nonlinear model predictive control in an offline framework. In this case and in the presence of unknown disturbances, the Lyapunov stability of the closed-loop system is guaranteed. Numerical simulations and comparative results verify the effectiveness of the proposed approach.
Citation Count: Baleanu, Dumitru...et.al. (2023). "A Weighted Average Finite Difference Scheme for the Numerical Solution of Stochastic Parabolic Partial Differential Equations", CMES - Computer Modeling in Engineering and Sciences, Vol.135, No.2, pp.1147-1163.
A Weighted Average Finite Difference Scheme for the Numerical Solution of Stochastic Parabolic Partial Differential Equations
(2023) Baleanu, Dumitru; Namjoo, Mehran; Mohebbian, Ali; Jajarmi, Amin; 56389
In the present paper, the numerical solution of Itô type stochastic parabolic equation with a time white noise process is imparted based on a stochastic finite difference scheme. At the beginning, an implicit stochastic finite difference scheme is presented for this equation. Some mathematical analyses of the scheme are then discussed. Lastly, to ascertain the efficacy and accuracy of the suggested technique, the numerical results are discussed and compared with the exact solution.
Citation Count: Baleanu, Dumitru; Hajipour, Mojtaba; Jajarmi, Amin, "An Efficient Nonstandard Finite Difference Scheme for a Class of Fractional Chaotic Systems", Journal of Computational and Nonlinear Dynamics, 13, No. 2, (2018).
An Efficient Nonstandard Finite Difference Scheme for a Class of Fractional Chaotic Systems
(ASME, 2018) Hajipour, Mojtaba; Jajarmi, Amin; Baleanu, Dumitru; 56389
In this paper, we formulate a new nonstandard finite difference (NSFD) scheme to study the dynamic treatments of a class of fractional chaotic systems. To design the new proposed scheme, an appropriate nonlocal framework is applied for the discretization of nonlinear terms. This method is easy to implement and preserves some important physical properties of the considered model, e.g., fixed points and their stability. Additionally, this scheme is explicit and inexpensive to solve fractional differential equations (FDEs). From a practical point of view, the stability analysis and chaotic behavior of three novel fractional systems are provided by the proposed approach. Numerical simulations and comparative results confirm that this scheme is also successful for the fractional chaotic systems with delay arguments.