Browsing by Author "Hajipour, Mojtaba"

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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: 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...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: Amiri, S.; Hajipour, M.; Baleanu, D.,"A Spectral Collocation Method With Piecewise Trigonometric Basis Functions for Nonlinear Volterra–Fredholm İntegral Equations", Applied Mathematics and Computation, Vol. 370, (2020).
A Spectral Collocation Method With Piecewise Trigonometric Basis Functions for Nonlinear Volterra–Fredholm İntegral Equations
(Elsevier INC, 2020) Amiri, Sadegh; Hajipour, Mojtaba; Baleanu, Dumitru; 56389
The aim of this paper is to investigate an efficient numerical method based on a novel shifted piecewise cosine basis for solving Volterra–Fredholm integral equations of the second kind. Using operational matrices of integration for the proposed basis functions, this integral equation is transformed into a system of nonlinear algebraic equations. The convergence and error analysis of the proposed method are studied. Some comparative results are provided to verify the efficiency of the presented method.
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.
Citation Count: Baleanu, Dumitru...et al. (2018). New aspects of poor nutrition in the life cycle within the fractional calculus, Advances in Difference Equations.
New aspects of poor nutrition in the life cycle within the fractional calculus
(Springer Open, 2018) Baleanu, Dumitru; Jajarmi, Amin; Bonyah, Ebenezer; Hajipour, Mojtaba; 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 Count: Jajarmi, A., Hajipour, M., Baleanu, D. (2017). New aspects of the adaptive synchronization and hyperchaos suppression of a financial model. Chaos Solutions&Fractals, 99, 285-296.http://dx.doi.org/ 10.1016/j.chaos.2017.04.025
New aspects of the adaptive synchronization and hyperchaos suppression of a financial model
(Pergamon-Elsevier Science, 2017) Jajarmi, Amin; Hajipour, Mojtaba; Baleanu, Dumitru
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.
Citation Count: Amiri, Sadegh; Hajipour, Mojtaba; Baleanu, Dumitru (2020). "On accurate solution of the Fredholm integral equations of the second kind", Applied Numerical Mathematics, Vol. 150, pp. 478-490.
On accurate solution of the Fredholm integral equations of the second kind
(2020) Amiri, Sadegh; Hajipour, Mojtaba; Baleanu, Dumitru; 56389
In this paper, an accurate numerical method based on the cosine-trigonometric basis functions is developed to solve the Fredholm integral equations of the second kind. By using the proposed method, the presented equation is converted into a system of algebraic equations. The convergence analysis of the proposed method is also investigated. To demonstrate the efficiency of the proposed method, the numerical simulations of various types of one- and two-dimensional examples are prepared. Comparative results show that this method is accurate than the other existing methods in the literature. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.
Citation Count: Hajipour, Mojtaba...et al. (20199. "On an accurate discretization of a variable-order fractional reaction-diffusion equation", Communications in Nonlinear Science And Numerical Simulation, Vol. 69, pp. 119-133.
On an accurate discretization of a variable-order fractional reaction-diffusion equation
(Elsevier Science BV, 2019) Hajipour, Mojtaba; Jajarmi, Amin; Baleanu, Dumitru; Sun, HongGuang; 56389
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 Count: Hajipour, Mojtaba; Jajarmi, Amin; Baleanu, Dumitru, "On the accurate discretization of a highly nonlinear boundary value problem", Numerical Algorithms, Vol. 79, No.3, pp. 679-695, (2018).
On the accurate discretization of a highly nonlinear boundary value problem
(Springer, 2018) Hajipour, Mojtaba; Jajarmi, Amin; Baleanu, Dumitru; 56389
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.
Citation Count: Hajipour, Ahamad; Hajipour, Mojtaba; Baleanu, Dumitru, "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system", Physica A-Statistıcal Mechanics and Its Applications, Vol. 497, pp. 139-153, (2018)
On the Adaptive Sliding Mode Controller for A Hyperchaotic Fractional-Order Financial System
(Elsevier Science BV, 2018) Hajipour, Ahamad; Hajipour, Mojtaba; Baleanu, Dumitru; 56389
This manuscript mainly focuses on the construction, dynamic analysis and control of a new fractional-order financial system. The basic dynamical behaviors of the proposed system are studied such as the equilibrium points and their stability, Lyapunov exponents, bifurcation diagrams, phase portraits of state variables and the intervals of system parameters. It is shown that the system exhibits hyperchaotic behavior for a number of system parameters and fractional-order values. To stabilize the proposed hyperchaotic fractional system with uncertain dynamics and disturbances, an efficient adaptive sliding mode controller technique is developed. Using the proposed technique, two hyperchaotic fractional-order financial systems are also synchronized. Numerical simulations are presented to verify the successful performance of the designed controllers. (C) 2018 Elsevier B.V. All rights reserved.
Citation Count: Baleanu, Dumitru; Jajarmi, Amin; Hajipour, Mojtaba, "On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag-Leffler kernel", Nonlinear Dynamics, Vol. 94, No. 1, pp. 397-414, (2018).
On the nonlinear dynamical systems within the generalized fractional derivatives with Mittag-Leffler kernel
(Springer, 2018) Baleanu, Dumitru; Jajarmi, Amin; Hajipour, Mojtaba; 56389
The purpose of this paper is to study the existence and uniqueness of the solution of nonlinear fractional differential equations with Mittag-Leffler nonsingular kernel. Two numerical methods to solve this problem are designed, and their stability and error estimates are investigated by discretizing the convolution integral and using the Gronwall's inequality. Finally, the theoretical results are verified by using five illustrative examples.
Citation Count: Hajipour, Mojtaba...et al. (2018). "Positivity-preserving sixth-order implicit finite difference weighted essentially non-oscillatory scheme for the nonlinear heat equation", Applied Mathematıcs and Computation, Vol. 325, pp. 146-158.
Positivity-Preserving Sixth-Order Implicit Finite Difference Weighted Essentially Non-Oscillatory Scheme for the Nonlinear Heat Equation
(Elsevier Science INC, 2018) Hajipour, Mojtaba; Jajarmi, Amin; Malek, Alaeddin; Baleanu, Dumitru; 56389
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 Count: Kheirkhah, Farnaz; Hajipour, Mojtaba; Baleanu, D. (2022). "The performance of a numerical scheme on the variable-order time-fractional advection-reaction-subdiffusion equations", Applied Numerical Mathematics, Vol.178, pp.25-40.
The performance of a numerical scheme on the variable-order time-fractional advection-reaction-subdiffusion equations
(2022) Kheirkhah, Farnaz; Hajipour, Mojtaba; Baleanu, Dumitru; 56389
This paper is concerned with a highly accurate numerical scheme for a class of one- and two-dimensional time-fractional advection-reaction-subdiffusion equations of variable-order α(x,t)∈(0,1). For the spatial and temporal discretization of the equation, a fourth-order compact finite difference operator and a third-order weighted-shifted Grünwald formula are applied, respectively. The stability and convergence of the present scheme are addressed. Some extensive numerical experiments are performed to confirm the theoretical analysis and high-accuracy of this novel scheme. Comparisons are also made with the available schemes in the literature.