Browsing by Author "Jajarmi, Amin"

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Citation - WoS: 94
Citation - Scopus: 110
Analysis and Some Applications of a Regularized Ψ-Hilfer Fractional Derivative
(Elsevier, 2022) Jajarmi, Amin; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Nieto, Juan J.
The main purpose of this research is to present a generalization of Psi-Hilfer fractional derivative, called as regularized Psi-Hilfer, and study some of its basic characteristics. In this direction, we show that the psi-Riemann-Liouville integral is the inverse operation of the presented regularized differentiation by means of the same function psi. In addition, we consider an initial-value problem comprising this generalization and analyze the existence as well as the uniqueness of its solution. To do so, we first present an approximation sequence via a successive substitution approach; then we prove that this sequence converges uniformly to the unique solution of the regularized Psi-Hilfer fractional differential equation (FDE). To solve this FDE, we suggest an efficient numerical scheme and show its accuracy and efficacy via some real-world applications. Simulation results verify the theoretical consequences and show that the regularized Psi-Hilfer fractional mathematical system provides a more accurate model than the other kinds of integer- and fractional-order differential equations. (C) 2022 Elsevier B.V. All rights reserved.
Citation - WoS: 72
Citation - Scopus: 87
An Efficient Nonstandard Finite Difference Scheme for a Class of Fractional Chaotic Systems
(Asme, 2018) Jajarmi, Amin; Baleanu, Dumitru; Hajipour, Mojtaba; 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.
Citation - WoS: 81
Citation - Scopus: 94
The Fractional Dynamics of a Linear Triatomic Molecule
(Editura Acad Romane, 2021) Baleanu, Dumitru; Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Defterli, Özlem; Jajarmi, Amin; Defterli, Ozlem; Asad, Jihad H.; 56389; Matematik
In this research, we study the dynamical behaviors of a linear triatomic molecule. First, a classical Lagrangian approach is followed which produces the classical equations of motion. Next, the generalized form of the fractional Hamilton equations (FHEs) is formulated in the Caputo sense. A numerical scheme is introduced based on the Euler convolution quadrature rule in order to solve the derived FHEs accurately. For different fractional orders, the numerical simulations are analyzed and investigated. Simulation results indicate that the new aspects of real-world phenomena are better demonstrated by considering flexible models provided within the use of fractional calculus approaches.
Citation - WoS: 131
Citation - Scopus: 152
The Fractional Features of a Harmonic Oscillator With Position-Dependent Mass
(Iop Publishing Ltd, 2020) Jajarmi, Amin; Sajjadi, Samaneh Sadat; Asad, Jihad H.; Baleanu, Dumitru; 56389
In this study, a harmonic oscillator with position-dependent mass is investigated. Firstly, as an introduction, we give a full description of the system by constructing its classical Lagrangian; thereupon, we derive the related classical equations of motion such as the classical Euler-Lagrange equations. Secondly, we fractionalize the classical Lagrangian of the system, and then we obtain the corresponding fractional Euler-Lagrange equations (FELEs). As a final step, we give the numerical simulations corresponding to the FELEs within different fractional operators. Numerical results based on the Caputo and the Atangana-Baleanu-Caputo (ABC) fractional derivatives are given to verify the theoretical analysis.
Citation - WoS: 24
Citation - Scopus: 24
Fractional Investigation of Time-Dependent Mass Pendulum
(Sage Publications Ltd, 2024) Defterli, Ozlem; Wannan, Rania; Sajjadi, Samaneh S.; Asad, Jihad H.; Baleanu, Dumitru; Jajarmi, Amin; 56389; 31401
In this paper, we aim to study the dynamical behaviour of the motion for a simple pendulum with a mass decreasing exponentially in time. To examine this interesting system, we firstly obtain the classical Lagrangian and the Euler-Lagrange equation of the motion accordingly. Later, the generalized Lagrangian is constructed via non-integer order derivative operators. The corresponding non-integer Euler-Lagrange equation is derived, and the calculated approximate results are simulated with respect to different non-integer orders. Simulation results show that the motion of the pendulum with time-dependent mass exhibits interesting dynamical behaviours, such as oscillatory and non-oscillatory motions, and the nature of the motion depends on the order of non-integer derivative; they also demonstrate that utilizing the fractional Lagrangian approach yields a model that is both valid and flexible, displaying various properties of the physical system under investigation. This approach provides a significant advantage in understanding complex phenomena, which cannot be achieved through classical Lagrangian methods. Indeed, the system characteristics, such as overshoot, settling time, and peak time, vary in the fractional case by changing the value of & alpha;. Also, the classical formulation is recovered by the corresponding fractional model when & alpha; tends to 1, while their output specifications are completely different. These successful achievements demonstrate diverse properties of physical systems, enhancing the adaptability and effectiveness of the proposed scheme for modelling complex dynamics.
Citation - WoS: 66
Citation - Scopus: 69
The Fractional Model of Spring Pendulum: New Features Within Different Kernels
(Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; 56389; Matematik
In this work, new aspects of the fractional calculus (FC) are examined for a model of spring pendulum in fractional sense. First, we obtain the classical Lagrangian of the model, and as a result, we derive the classical Euler-Lagrange equations of the motion. Second, we generalize the classical Lagrangian to fractional case and derive the fractional Euler-Lagrange equations in terms of fractional derivatives with singular and nonsingular kernels, respectively. Finally, we provide the numerical solution of these equations within two fractional operators for some fractional orders and initial conditions. Numerical simulations verify that taking into account the recently features of the FC provides more realistic models demonstrating hidden aspects of the real-world phenomena.
Citation - WoS: 104
Citation - Scopus: 117
Fractional Treatment: an Accelerated Mass-Spring System
(Editura Acad Romane, 2022) Defterli, Ozlem; Baleanu, Dumitru; Baleanu, Dumitru; Defterli, Özlem; Jajarmi, Amin; Sajjadi, Samaneh Sadat; Alshaikh, Noorhan; Asad, Jihad H.; 56389; 31401; Matematik
The aim of this manuscript is to study the dynamics of the motion of an accelerated mass-spring system within fractional calculus. To investigate the described system, firstly, we construct the corresponding Lagrangian and derive the classical equations of motion using the Euler-Lagrange equations of integer-order. Furthermore, the generalized Lagrangian is introduced by using non-integer, so-called fractional, derivative operators; then the resulting fractional Euler-Lagrange equations are generated and solved numerically. The obtained results are presented illustratively by using numerical simulations.
Citation - WoS: 123
Citation - Scopus: 142
A General Fractional Formulation and Tracking Control for Immunogenic Tumor Dynamics
(Wiley, 2022) Baleanu, Dumitru; Vahid, Kianoush Zarghami; Mobayen, Saleh; Jajarmi, Amin; 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 - WoS: 117
Citation - Scopus: 135
Hyperchaotic Behaviors, Optimal Control, and Synchronization of a Nonautonomous Cardiac Conduction System
(Springer, 2021) Sajjadi, Samaneh Sadat; Asad, Jihad H.; Jajarmi, Amin; Estiri, Elham; Baleanu, Dumitru; 56389
In this paper, the hyperchaos analysis, optimal control, and synchronization of a nonautonomous cardiac conduction system are investigated. We mainly analyze, control, and synchronize the associated hyperchaotic behaviors using several approaches. More specifically, the related nonlinear mathematical model is firstly introduced in the forms of both integer- and fractional-order differential equations. Then the related hyperchaotic attractors and phase portraits are analyzed. Next, effectual optimal control approaches are applied to the integer- and fractional-order cases in order to overcome the obnoxious hyperchaotic performance. In addition, two identical hyperchaotic oscillators are synchronized via an adaptive control scheme and an active controller for the integer- and fractional-order mathematical models, respectively. Simulation results confirm that the new nonlinear fractional model shows a more flexible behavior than its classical counterpart due to its memory effects. Numerical results are also justified theoretically, and computational experiments illustrate the efficacy of the proposed control and synchronization strategies.
Infectious Disease Dynamics within Advanced Fractional Operators
(2019) Defterli, Özlem; Arshad, Sadia; Jajarmi, Amin; 31401
Citation - WoS: 167
Citation - Scopus: 206
A New Adaptive Synchronization and Hyperchaos Control of a Biological Snap Oscillator
(Pergamon-elsevier Science Ltd, 2020) Baleanu, Dumitru; Jajarmi, Amin; Pirouz, Hassan Mohammadi; Sajjadi, Samaneh Sadat; 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 - WoS: 171
Citation - Scopus: 182
A New and Efficient Numerical Method for the Fractional Modeling and Optimal Control of Diabetes and Tuberculosis Co-Existence
(Amer inst Physics, 2019) Ghanbari, Behzad; Baleanu, Dumitru; Jajarmi, Amin; 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 - WoS: 64
Citation - Scopus: 69
A New Approach for the Nonlinear Fractional Optimal Control Problems With External Persistent Disturbances
(Pergamon-elsevier Science Ltd, 2018) Hajipour, Mojtaba; Mohammadzadeh, Ehsan; Baleanu, Dumitru; Jajarmi, Amin; 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 - WoS: 16
Citation - Scopus: 17
A New Approach for the Optimal Control of Time-Varying Delay Systems With External Persistent Matched Disturbances
(Sage Publications Ltd, 2018) Hajipour, Mojtaba; Baleanu, Dumitru; Jajarmi, Amin; 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 - WoS: 90
Citation - Scopus: 110
New Aspects of Poor Nutrition in the Life Cycle Within the Fractional Calculus
(Springer, 2018) Jajarmi, Amin; Bonyah, Ebenezer; Hajipour, Mojtaba; Baleanu, Dumitru; 56389
The nutrition of pregnant women is crucial for giving birth to a healthy baby and even for the health status of a nursing mother. In this paper, the poor nutrition in the life cycle of humans is explored in the fractional sense. The proposed model is examined via the Caputo fractional operator and a new one with Mittag-Leffler (ML) nonsingular kernel. The stability analysis as well as the existence and uniqueness of the solution are investigated, and an efficient numerical scheme is also designed for the approximate solution. Comparative numerical analysis of these two operators reveals that the model based on the new fractional derivative with ML kernel has a different asymptotic behavior to the classic Caputo. Thus, the new aspects of fractional calculus provide more flexible models which help us to adjust the dynamical behaviors of the real-world phenomena better.
Citation - WoS: 93
Citation - Scopus: 103
New Aspects of the Adaptive Synchronization and Hyperchaos Suppression of a Financial Model
(Pergamon-elsevier Science Ltd, 2017) Hajipour, Mojtaba; Baleanu, Dumitru; Jajarmi, Amin
This paper mainly focuses on the analysis of a hyperchaotic financial system as well as its chaos control and synchronization. The phase diagrams of the above system are plotted and its dynamical behaviours like equilibrium points, stability, hyperchaotic attractors and Lyapunov exponents are investigated. In order to control the hyperchaos, an efficient optimal controller based on the Pontryagin's maximum principle is designed and an adaptive controller established by the Lyapunov stability theory is also implemented. Furthermore, two identical financial models are globally synchronized by using an interesting adaptive control scheme. Finally, a fractional economic model is introduced which can also generate hyperchaotic attractors. In this case, a linear state feedback controller together with an active control technique are used in order to control the hyperchaos and realize the synchronization, respectively. Numerical simulations verifying the theoretical analysis are included. (C) 2017 Elsevier Ltd. All rights reserved.
Citation - WoS: 59
Citation - Scopus: 66
New Aspects of the Motion of a Particle in a Circular Cavity
(Editura Acad Romane, 2018) Baleanu, Dumitru; Baleanu, Dumitru; Asad, Jihad H.; Jajarmi, Amin; 56389; Matematik
In this work, we consider the free motion of a particle in a circular cavity. For this model, we obtain the classical and fractional Lagrangian as well as the fractional Hamilton's equations (FHEs) of motion. The fractional equations are formulated in the sense of Caputo and a new fractional derivative with Mittag-Leffler nonsingular kernel. Numerical simulations of the FHEs within these two fractional operators are presented and discussed for some fractional derivative orders. Numerical results are based on a discretization scheme using the Euler convolution quadrature rule for the discretization of the convolution integral. Simulation results show that the fractional calculus provides more flexible models demonstrating new aspects of the real-world phenomena.
Citation - WoS: 87
Citation - Scopus: 93
New Aspects of Time Fractional Optimal Control Problems Within Operators With Nonsingular Kernel
(Amer inst Mathematical Sciences-aims, 2020) Jajarmi, Amin; Yildiz, Burak; Baleanu, Dumitru; Yildiz, Tugba Akman; 56389
This paper deals with a new formulation of time fractional optimal control problems governed by Caputo-Fabrizio (CF) fractional derivative. The optimality system for this problem is derived, which contains the forward and backward fractional differential equations in the sense of CF. These equations are then expressed in terms of Volterra integrals and also solved by a new numerical scheme based on approximating the Volterra integrals. The linear rate of convergence for this method is also justified theoretically. We present three illustrative examples to show the performance of this method. These examples also test the contribution of using CF derivative for dynamical constraints and we observe the efficiency of this new approach compared to the classical version of fractional operators.
Citation - WoS: 99
Citation - Scopus: 123
A New Feature of the Fractional Euler-Lagrange Equations for a Coupled Oscillator Using a Nonsingular Operator Approach
(Frontiers Media Sa, 2019) Baleanu, Dumitru; Sajjadi, Samaneh Sadat; Asad, Jihad H.; Jajarmi, Amin; 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.
Citation - WoS: 98
Citation - Scopus: 104
New Features of the Fractional Euler-Lagrange Equations for a Physical System Within Non-Singular Derivative Operator
(Springer Heidelberg, 2019) Sajjadi, Samaneh Sadat; Jajarmi, Amin; Asad, Jihad H.; Baleanu, Dumitru; 56389
.Free motion of a fractional capacitor microphone is investigated in this paper. First, a capacitor microphone is introduced and the Euler-Lagrange equations are established. Due to the fractional derivative's the history independence, the fractional order displacement and electrical charge are used in the equations. Fractional differential equations involve in the right- and left-hand-sided derivatives which is reduced to a boundary value problem. Finally, numerical simulations are obtained and dynamical behaviors are numerically discussed.