7 results on '"ETEMAD, SINA"'
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2. Some novel mathematical analysis on the fractal–fractional model of the AH1N1/09 virus and its generalized Caputo-type version.
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Etemad, Sina, Avci, Ibrahim, Kumar, Pushpendra, Baleanu, Dumitru, and Rezapour, Shahram
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MATHEMATICAL analysis , *STABILITY criterion , *INFLUENZA A virus , *FRACTAL analysis , *INFLUENZA viruses - Abstract
In this paper, we formulate a new model of a particular type of influenza virus called AH1N1/09 in the framework of the four classes consisting of susceptible, exposed, infectious and recovered people. For the first time, we here investigate this model with the help of the advanced operators entitled the fractal–fractional operators with two fractal and fractional orders via the power law type kernels. The existence of solution for the mentioned fractal–fractional model of AH1N1/09 is studied by some special mappings such as ϕ − ψ -contractions and ϕ -admissibles. The Leray–Schauder theorem is also applied for this aim. After investigating the stability criteria in four versions, to approximate the desired numerical solutions, we implement Adams–Bashforth (AB) scheme and simulate the graphs for different data on the fractal and fractional orders. Lastly, we convert our fractal–fractional AH1N1/09 model into a fractional model via the generalized Liouville–Caputo-type (GLC-type) operators and then, we simulate new graphs caused by the new numerical scheme called Kumar–Erturk method. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
3. A novel modeling of boundary value problems on the glucose graph.
- Author
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Baleanu, Dumitru, Etemad, Sina, Mohammadi, Hakimeh, and Rezapour, Shahram
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BOUNDARY value problems , *GLUCOSE , *REPRESENTATIONS of graphs , *CAPUTO fractional derivatives , *MOLECULAR structure - Abstract
• Main novelty of this work is using boundary value probems on the graph of the Glucose molecule. • We use modern nonlinear technique for provig of the solution of the sysem. • We use a new technique for numeing of the graph of the Glucose molecule to could start our techniques. • We provide an illustraing example. In this article, with due attention to a new labeling method for vertices of arbitrary graphs, we investigate the existence results for a novel modeling of the fractional multi-term boundary value problems on each edge of the graph representation of the Glucose molecule. In this direction, we consider a graph with labeled vertices by 0 or 1 inspired by the molecular structure of the Glucose molecule and then derive some existence results by applying two known fixed point theorems. Finally, we provide an example to illustrate the validity of our main result. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
4. Trajectory tracking of Stanford robot manipulator by fractional-order sliding mode control.
- Author
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Chávez-Vázquez, Samuel, Lavín-Delgado, Jorge E., Gómez-Aguilar, José F., Razo-Hernández, José R., Etemad, Sina, and Rezapour, Shahram
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SLIDING mode control , *FRACTIONAL calculus , *FRACTIONAL integrals , *MANIPULATORS (Machinery) , *INDUCTION motors , *SYSTEM dynamics , *ROBOTS - Abstract
• Fractional control law for the Stanford robot for tracking trajectory tasks is proposed. • Coupled system is composed of the robot manipulator and the actuators of the joints consider induction motors. • Dynamics of the system are obtained by the Euler–Lagrange method and generalized through the Caputo Fabrizio derivative. • Fractional integral sliding mode control via the Caputo–Fabrizio derivative for trajectory tracking control. • Introduction of AB- integral in the fractional sliding surface improving controller performance. In this work, a fractional integral sliding-mode control scheme based on the Caputo–Fabrizio derivative and the Atangana–Baleanu integral of the Stanford robot for trajectory tracking tasks is developed and presented. The coupled system is composed of the robot manipulator and the induction motors that drive its joints. The mathematical model of the system is obtained by the Euler–Lagrange method and generalized to an arbitrary order via the Caputo–Fabrizio derivative. The actuators are controlled by fractional PI controllers based on the Atangana–Baleanu integral, while a fractional integral sliding mode control law is also developed for trajectory tracking control. In this context, a fractional version of the sliding surface via the Caputo–Fabrizio derivative is introduced to improve the performance of the control system. In addition, to attenuate the chattering effects, a fractional integral term, based on the Atangana–Baleanu integral, is introduced on the sliding surface further improving system performance with less power consumption. The conventional integral sliding mode control and an optimal super-twisting sliding mode control are also introduced for comparison with the proposed control strategy. The control schemes were tuned using the Cuckoo method. External disturbances are also considered in the system dynamics, as well as different end-effector reference trajectories, which were designed to carry out manufacturing tasks. Simulation results confirm the superiority of our control scheme for trajectory-tracking applications over its conventional version and the optimal super-twisting sliding mode control, even with external disturbances and trajectory changes. To show the robustness of the proposed control scheme under different operating conditions, all the numerical simulations were performed considering the same orders and gains. Finally, our control law introduces the fractional derivative and integral of Caputo–Fabrizio and Atangana–Baleanu respectively, which have not been used enough in the modeling and control of robotic systems. Therefore, it is interesting to analyze the contributions and advantages that arise when using them. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
5. A case study of fractal-fractional tuberculosis model in China: Existence and stability theories along with numerical simulations.
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Khan, Hasib, Alam, Khurshaid, Gulzar, Haseena, Etemad, Sina, and Rezapour, Shahram
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STABILITY theory , *TUBERCULOSIS , *COMPUTER simulation , *NUMERICAL analysis , *MATHEMATICAL models , *FRACTAL analysis - Abstract
In this article, a fractal-fractional order tuberculosis mathematical model is presented for the existence results, numerical simulations and stability analysis. The model has six classes S 1 , S 2 , S 3 , E , I , R. The first three classes S 1 , S 2 , S 3 represent the population of susceptible children, middle-aged, and senior adults, respectively. While I is the class of active infected individuals who can transmit the tuberculosis, E stands for non-active infected class. The population of recovered individuals is represented by R. For the existence criterion of the given model, successive iterative sequences are defined whose limit points are the solutions of our proposed tuberculosis model. After investigation of uniqueness property, the Hyers–Ulam (HU)-stability is established in the sequel. With the help of two-step Lagrange polynomials, we provide numerical solutions and we give a comparative numerical analysis for different values of the fractional order and fractal order based on the obtained algorithms. The numerical simulations show the applicability of the schemes and the future prediction. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
6. Dynamics of a model of polluted lakes via fractal–fractional operators with two different numerical algorithms.
- Author
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Kanwal, Tanzeela, Hussain, Azhar, Avcı, İbrahim, Etemad, Sina, Rezapour, Shahram, and Torres, Delfim F.M.
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LAKES , *WATER pollution , *FRACTALS - Abstract
We employ Mittag-Leffler type kernels to solve a system of fractional differential equations using fractal–fractional (FF) operators with two fractal and fractional orders. Using the notion of FF-derivatives with nonsingular and nonlocal fading memory, a model of three polluted lakes with one source of pollution is investigated. The properties of a non-decreasing and compact mapping are used in order to prove the existence of a solution for the FF-model of polluted lake system. For this purpose, the Leray–Schauder theorem is used. After exploring stability requirements in four versions, the proposed model of polluted lakes system is then simulated using two new numerical techniques based on Adams–Bashforth and Newton polynomials methods. The effect of fractal–fractional differentiation is illustrated numerically. Moreover, the effect of the FF-derivatives is shown under three specific input models of the pollutant: linear, exponentially decaying, and periodic. • Mittag-Leffler fractal–fractional (FF) modeling of polluted lakes. • Well posedness of the polluted lake system with nonsingular and nonlocal fading memory. • Stability of the polluted lakes system. • New numerical techniques based on Adams–Bashforth and Newton polynomials methods. • The effect of linear, exponentially decaying, and periodic pollutants. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
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7. A theoretical study of the Caputo–Fabrizio fractional modeling for hearing loss due to Mumps virus with optimal control.
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Mohammadi, Hakimeh, Kumar, Sunil, Rezapour, Shahram, and Etemad, Sina
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BASIC reproduction number , *HEARING disorders , *FIXED point theory , *MUMPS , *EULER method , *INFECTIOUS disease transmission - Abstract
Mumps is the most common cause of acquired unilateral deafness in children, in which hearing loss occurs at all auditory frequencies. We use a box model to model hearing loss in children caused by the mumps virus, and since the fractional-order derivative retains the effect of system memory, we use the Caputo–Fabrizio fractional derivative in this modeling. In the beginning, we compute the basic reproduction number R 0 and equilibrium points of the system and investigate the stability of the system at the equilibrium point. By utilizing the Picard–Lindelof technique, we prove the existence an unique solution for given fractional CF -system of hearing loss model and investigate the stability of iterative method by fixed point theory. The optimal control of the system is determined by considering the treatment as a control strategy to reduce the number of infected people. Using the Euler method for the fractional-order Caputo–Fabrizio derivative, the approximate solution of the system is calculated. We present a numerical simulation for the transmission of disease with respect to the transmission rate and the basic reproduction number in two cases R 0 < 1 and R 0 > 1. To investigate the effect of fractional order derivative on the behavior and value of each of the variables in Model 2, we calculate the results for several fractional order derivatives and compare the results. Also, considering the importance of reproduction number in the continuation of disease transmission, we analyze the sensitivity of R 0 respect to each of the model parameters and determine the impact of each parameter. [ABSTRACT FROM AUTHOR]
- Published
- 2021
- Full Text
- View/download PDF
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