Browsing by Author "Jajarmi, Amin"

Now showing 1 - 20 of 42

Citation - WoS: 74
Citation - Scopus: 81
On the Accurate Discretization of a Highly Nonlinear Boundary Value Problem
(Springer, 2018) Jajarmi, Amin; Baleanu, Dumitru; Hajipour, Mojtaba
The aim of this manuscript is to investigate an accurate discretization method to solve the one-, two-, and three-dimensional highly nonlinear Bratu-type problems. By discretization of the nonlinear equation via a fourth-order nonstandard compact finite difference formula, the considered problem is reduced to the solution of a highly nonlinear algebraic system. To solve the derived nonlinear system, a modified nonlinear solver is used. The new scheme is accurate, fast, straightforward and very effective to find the lower and upper branches of the Bratu's problem. Numerical simulations and comparative results for the one-, two-, and three-dimensional cases verify that the new technique is easy to implement and more accurate than the other existing methods in the literature.
Infectious Disease Dynamics within Advanced Fractional Operators
(2019) Defterli, Özlem; Arshad, Sadia; Jajarmi, Amin
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
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: 131
Citation - Scopus: 148
On an Accurate Discretization of a Variable-Order Fractional Reaction-Diffusion Equation
(Elsevier Science Bv, 2019) Jajarmi, Amin; Baleanu, Dumitru; Sun, HongGuang; Hajipour, Mojtaba
The aim of this paper is to develop an accurate discretization technique to solve a class of variable-order fractional (VOF) reaction-diffusion problems. In the spatial direction, the problem is first discretized by using a compact finite difference operator. Then, a weighted-shifted Grunwald formula is applied for the temporal discretization of fractional derivatives. To solve the derived nonlinear discrete system, an accurate iterative algorithm is also formulated. The solvability, stability and L-2-convergence of the proposed scheme are derived for all variable-order alpha(t) is an element of (0, 1). The proposed method is of accuracy-order O(tau(3) + h(4)), where tau and h are temporal and spatial step sizes, respectively. Through some numerical simulations, the theoretical analysis and high-accuracy of the proposed method are verified. Comparative results also indicate that the accuracy of the new discretization technique is superior to the other methods available in the literature. Finally, the feasibility of the proposed VOF model is demonstrated by using the reported experimental data. (C) 2018 Elsevier B.V. All rights reserved.
Citation - WoS: 79
Citation - Scopus: 92
A New Formulation of the Fractional Optimal Control Problems Involving Mittag-Leffler Nonsingular Kernel
(Springer/plenum Publishers, 2017) Jajarmi, Amin; Hajipour, Mojtaba; Baleanu, Dumitru
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 - WoS: 67
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; 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: 14
Citation - Scopus: 18
Optimal Control of Nonlinear Dynamical Systems Based on a New Parallel Eigenvalue Decomposition Approach
(Wiley, 2018) Baleanu, Dumitru; Jajarmi, Amin
This manuscript aims to investigate a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. For this purpose, a sequence of decoupled linear two-point boundary value problems is solved iteratively instead of solving the coupled nonlinear two-point boundary value problem derived from the maximum principle. The convergence analysis of the suggested technique is also investigated. In addition, the problem that needs to be solved at each iteration is composed of lower-order decoupled subproblems; hence, they can be solved in parallel. Thus, the new scheme has a parallel computing property improving its computational effectiveness. Numerical simulations and comparative results show that the proposed approach is efficient and provides satisfactory results.
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; 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: 99
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
.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.
Citation - WoS: 131
Citation - Scopus: 153
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
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: 172
Citation - Scopus: 210
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
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: 76
Citation - Scopus: 86
Positivity-Preserving Sixth-Order Implicit Finite Difference Weighted Essentially Non-Oscillatory Scheme for the Nonlinear Heat Equation
(Elsevier Science inc, 2018) Jajarmi, Amin; Malek, Alaeddin; Baleanu, Dumitru; Hajipour, Mojtaba
This paper presents a class of semi-implicit finite difference weighted essentially non-oscillatory (WENO) schemes for solving the nonlinear heat equation. For the discretization of second-order spatial derivatives, a sixth-order modified WENO scheme is directly implemented. This scheme preserves the positivity principle and rejects spurious oscillations close to non-smooth points. In order to admit large time steps, a class of implicit Runge-Kutta methods is used for the temporal discretization. The implicit parts of these methods are linearized in time by using the local Taylor expansion of the flux. The stability analysis of the semi-implicit WENO scheme with 3-stages form is provided. Finally, some comparative results for one-, two-and three-dimensional PDEs are included to illustrate the effectiveness of the proposed approach. (c) 2017 Elsevier Inc. All rights reserved.
Citation - WoS: 125
Citation - Scopus: 137
A New Fractional Hrsv Model and Its Optimal Control: A Non-Singular Operator Approach
(Elsevier, 2020) Yusuf, Abdullahi; Baleanu, Dumitru; Inc, Mustafa; Jajarmi, Amin
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 a 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. (C) 2019 Elsevier B.V. All rights reserved.
Citation - WoS: 172
Citation - Scopus: 183
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
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: 126
Citation - Scopus: 139
Planar System-Masses in an Equilateral Triangle: Numerical Study Within Fractional Calculus
(Tech Science Press, 2020) Ghanbari, Behzad; Asad, Jihad H.; Jajarmi, Amin; Pirouz, Hassan Mohammadi; Baleanu, Dumitru
In this work, a system of three masses on the vertices of equilateral triangle is investigated. This system is known in the literature as a planar system. We first give a description to the system by constructing its classical Lagrangian. Secondly, the classical Euler-Lagrange equations (i.e., the classical equations of motion) are derived. Thirdly, we fractionalize the classical Lagrangian of the system, and as a result, we obtain the fractional Euler-Lagrange equations. As the final step, we give the numerical simulations of the fractional model, a new model which is based on Caputo fractional derivative.
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
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: 109
A New Intervention Strategy for an Hiv/Aids Transmission by a General Fractional Modeling and an Optimal Control Approach
(Pergamon-elsevier Science Ltd, 2023) Hasanabadi, Manijeh; Vaziri, Asadollah Mahmoudzadeh; Jajarmi, Amin; Baleanu, Dumitru
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 - WoS: 105
Citation - Scopus: 116
Stability Analysis and System Properties of Nipah Virus Transmission: a Fractional Calculus Case Study
(Pergamon-elsevier Science Ltd, 2023) Shekari, Parisa; Torkzadeh, Leila; Ranjbar, Hassan; Jajarmi, Amin; Nouri, Kazem; Baleanu, Dumitru
In this paper, we establish a Caputo-type fractional model to study the Nipah virus transmission dynamics. The model describes the impact of unsafe contact with an infectious corpse as a possible way to transmit this virus. The corresponding area to the system properties, including the positivity and boundedness of the solution, is explored by using the generalized fractional mean value theorem. Also, we investigate sufficient conditions for the local and global stability of the disease-free and the endemic steady-states based on the basic reproduction number R0. To show these important stability features, we employ fractional Routh-Hurwitz criterion and LaSalle's invariability principle. For the implementation of this epidemic model, we also use the Adams-Bashforth-Moulton numerical method in a fractional sense. Finally, in addition to compare the fractional and classical results, as one of the main goals of this research, we demonstrate the usefulness of minimal unsafe touch with the infectious corpse. Simulation and comparative results verify the theoretical discussions.
Citation - WoS: 65
Citation - Scopus: 70
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
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: 171
Citation - Scopus: 172
On the Fractional Optimal Control Problems With a General Derivative Operator
(Wiley, 2021) Baleanu, Dumitru; Jajarmi, Amin
This paper deals with a general form of fractional optimal control problems involving the fractional derivative with singular or non-singular kernel. The necessary conditions for the optimality of these problems are derived and a new numerical method is designed to solve these equations effectively. Simulation results indicate that the proposed method works well and provides satisfactory results with regard to accuracy and computational effort. Comparative results also verify that a particular case with Mittag-Leffler kernel improves the performance of the controlled system in terms of the transient response compared to the other fractional- and integer-order derivatives.