scholarly journals Study of electrical R-L circuits composed of resistors and inductors and driven by a voltage of the current source: Simulation with implementing an accurate method

2020 ◽  
Author(s):  
Mohamed Adel ◽  
Hari M. Srivastava ◽  
Mohamed Khader
Keyword(s):  
Current Source ◽  
Numerical Procedure ◽  
Classical Case ◽  
Approximate Solutions ◽  
Accurate Method ◽  
Order Model ◽  
The Third ◽  
Fractional Order Model ◽  
Proposed Model ◽  
The Mathematical Model

In this study, we propose to derive an accurate numerical procedure to solve the mathematical model which describes the electrical R-L circuit composed of resistors and inductors driven by a voltage of current source, which is the fractional-order model for the electrical RL-circuit. Our study depends on the spectral collocation method via the useful properties of the Chebyshev polynomials of the third-kind. Some theorems about the convergence analysis are given. The study concludes by comparing the resulting approximate solutions of the proposed model with the exact solution in the classical case. Illustrative graphical and numerical analysis of the derived results are also included in this study.

scholarly journals Special function form exact solutions for Jeffery fluid: an application of power law kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Maryam Asgir ◽  
A. A. Zafar ◽  
Abdullah M. Alsharif ◽  
Muhammad Bilal Riaz ◽  
Muhammad Abbas
Keyword(s):  
Classical Model ◽  
Parallel Plates ◽  
Order Model ◽  
Physical Conditions ◽  
Fractional Order Model ◽  
Fluid Parameter ◽  
The Laplace Transform ◽  
The One ◽  
The Mathematical Model ◽  
Validation Of Results

AbstractThis research note’s objective is to elaborate on the study of the unsteady MHD natural convective flow of the Jeffery fluid with the fractional derivative model. The fluid flow phenomenon happens between two vertical parallel plates immersed in a porous medium. The one plate is moving with the time-dependent velocity $U_{0} f(t)$ U 0 f ( t ) , while the other is fixed. The mathematical model is presented with the system of the partial differential equation along with physical conditions. Appropriate dimensionless variables are employed in the system of equations, and then this dimensionless model is transformed into the Caputo fractional-order model and solved analytically by the Laplace transform. The exact expressions for velocity and temperature, which satisfy the imposed initial and boundary conditions, are obtained. Memory effects in the fluid are observed which the classical model fails to elaborate. Interesting results are revealed from the investigation of emerging parameters as Grashof number, Prandtl number, relaxation time parameter, Jeffery fluid parameter, Hartmann number, porosity, and fractional parameter. The results are elucidated with the detailed discussion and the assistance of the graphs. For the sake of validation of results, the corresponding solutions for viscous fluids are also obtained and compared with the solutions already existing in the literature.

scholarly journals Analytical Solutions for the Mathematical Model Describing the Formation of Liver Zones via Adomian’s Method

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdelhalim Ebaid
Keyword(s):  
Differential Equations ◽  
Decomposition Method ◽  
Applied Mathematics ◽  
Mathematical Formulation ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Stationary Solutions ◽  
Proposed Model ◽  
Adomian Decomposition ◽  
The Mathematical Model

The formation of liver zones is modeled by a system of two integropartial differential equations. In this research, we introduce the mathematical formulation of these integro-partial differential equations obtained by Bass et al. in 1987. For better understanding of this mathematical formulation, we present a medical introduction for the liver in order to make the formulation as clear as possible. In applied mathematics, the Adomian decomposition method is an effective procedure to obtain analytic and approximate solutions for different types of operator equations. This Adomian decomposition method is used in this work to solve the proposed model analytically. The stationary solutions (as time tends to infinity) are also obtained through it, which are in full agreement with those obtained by Bass et al. in 1987.

scholarly journals Dynamical Analysis of Approximate Solutions of HIV-1 Model with an Arbitrary Order

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Asma ◽  
Nigar Ali ◽  
Gul Zaman ◽  
Anwar Zeb ◽  
Vedat Suat Erturk ◽  
...  
Keyword(s):  
Fractional Order ◽  
Dynamical Behavior ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Dynamical Analysis ◽  
Order Model ◽  
Hiv Model ◽  
Fractional Order Model ◽  
Adomian Decomposition ◽  
Hiv 1

This article studies the dynamical behavior of the analytical solutions of the system of fraction order model of HIV-1 infection. For this purpose, first, the proposed integer order model is converted into fractional order model. Then, Laplace-Adomian decomposition method (L-ADM) is applied to solve this fractional order HIV model. Moreover, the convergence of this method is also discussed. It can be observed from the numerical solution that (L-ADM) is very simple and accurate to solve fraction order HIV model.

scholarly journals Numerical, Approximate Solutions, and Optimal Control on the Deathly Lassa Hemorrhagic Fever Disease in Pregnant Women

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
M. Higazy ◽  
A. El-Mesady ◽  
A. M. S. Mahdy ◽  
Sami Ullah ◽  
A. Al-Ghamdi
Keyword(s):  
Optimal Control ◽  
Pregnant Women ◽  
Fractional Order ◽  
Adomian Decomposition Method ◽  
Hemorrhagic Fever ◽  
Approximate Solutions ◽  
Order Model ◽  
Fractional Order Model ◽  
Adomian Decomposition ◽  
Negative Impacts

This paper is devoted to the model of Lassa hemorrhagic fever (LHF) disease in pregnant women. This disease is a biocidal fever and epidemic. LHF disease in pregnant women has negative impacts that were initially appeared in Africa. In the present study, we find an approximate solution to the fractional-order model that describes the fatal LHF disease. Laplace transforms coupled with the Adomian decomposition method (ADM) are applied. In addition, the fractional-order LHF model is numerically simulated in terms of a varied fractional order. Furthermore, a fractional order optimal control for the LHF model is studied.

scholarly journals Existence theory and numerical simulation of HIV-I cure model with new fractional derivative possessing a non-singular kernel

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Aliyu Isa Aliyu ◽  
Ali Saleh Alshomrani ◽  
Yongjin Li ◽  
Mustafa Inc ◽  
Dumitru Baleanu
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Numerical Technique ◽  
Research Work ◽  
Approximate Solutions ◽  
Existence Theory ◽  
Double Precision ◽  
Order Model ◽  
Invariant Region ◽  
Fractional Order Model

Abstract In this research work, a mathematical model related to HIV-I cure infection therapy consisting of three populations is investigated from the fractional calculus viewpoint. Fractional version of the model under consideration has been proposed. The proposed model is examined by using the Atangana–Baleanu fractional operator in the Caputo sense (ABC). The theory of Picard–Lindelöf has been employed to prove existence and uniqueness of the special solutions of the proposed fractional-order model. Further, it is also shown that the non-negative hyper-plane $\mathbb{R}_{+}^{3}$ R + 3 is a positively invariant region for the underlying model. Finally, to analyze the results, some numerical simulations are carried out via a numerical technique recently devised for finding approximate solutions of fractional-order dynamical systems. Upon comparison of the numerical simulations, it has been demonstrated that the proposed fractional-order model is more accurate than its classical version. All the necessary computations have been performed using MATLAB R2018a with double precision arithmetic.

scholarly journals Signal Smoothing with Time-Space Fractional Order Model

2021 ◽  
Vol 21 (1) ◽  
pp. 25-32
Author(s):  
Yuanlu Li
Keyword(s):  
Diffusion Model ◽  
Fractional Order ◽  
Order Model ◽  
Comparison Result ◽  
Smoothing Methods ◽  
Fractional Order Model ◽  
Time Space ◽  
Proposed Model ◽  
Noisy Signals ◽  
And Performance

Abstract The time-space fractional-order model (TSFOM) is a generation of the classical diffusion model which is an excellent smoothing method. In this paper, the fractional-order derivative in the model is found to have good performance for peak-preserving. To check the validity and performance of the model, some noisy signals are smoothed by some commonly used smoothing methods and results are compared with those of the proposed model. The comparison result shows that the proposed method outperforms the classical nonlinear diffusion model and some commonly used smoothing methods.

scholarly journals Dynamical analysis of fractional-order of IVGTT glucose–insulin interaction

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Mansoor H. Alshehri ◽  
Sayed Saber ◽  
Faisal Z. Duraihem
Keyword(s):  
Hopf Bifurcation ◽  
Fractional Order ◽  
Euler Method ◽  
Dynamical Analysis ◽  
Order Model ◽  
Insulin Metabolism ◽  
Fractional Order Model ◽  
Proposed Model ◽  
Predictor Corrector ◽  
Tolerance Testing

Abstract This paper proposes a fractional-order model of glucose–insulin interaction. In Caputo’s meaning, the fractional derivative is defined. This model arises in Bergman’s minimal model, used to describe blood glucose and insulin metabolism, after intravenous tolerance testing. We showed that the established model has existence, uniqueness, non-negativity, and boundedness of fractional-order model solutions. The model’s local and global stability was investigated. The parametric conditions under which a Hopf bifurcation occurs in the positive steady state for a proposed model are studied. Moreover, we present a numerical treatment for solving the proposed fractional model using the generalized Euler method (GEM). The model’s local stability and Hopf bifurcation of the proposed model in sense of the GEM are presented. Finally, numerical simulations of the model using the Adam–Bashforth–Moulton predictor corrector scheme and the GEM have been presented to support our analytical results.

scholarly journals Fractional Order Model of the Two Dimensional Heat Transfer Process

Energies ◽  
2021 ◽  
Vol 14 (19) ◽  
pp. 6371
Author(s):  
Krzysztof Oprzędkiewicz ◽  
Wojciech Mitkowski ◽  
Maciej Rosół
Keyword(s):  
Heat Transfer ◽  
Fractional Order ◽  
Heat Transfer Process ◽  
Two Dimensional ◽  
Thermal Camera ◽  
Order Model ◽  
Fractional Order Model ◽  
Proposed Model ◽  
Spectrum Decomposition ◽  
Theoretical Results

In this paper, a new, state space, fractional order model of a heat transfer in two dimensional plate is addressed. The proposed model derives directly from a two dimensional heat transfer equation. It employes the Caputo operator to express the fractional order differences along time. The spectrum decomposition and stability of the model are analysed. The formulae of impluse and step responses of the model are proved. Theoretical results are verified using experimental data from thermal camera. Comparison model vs experiment shows that the proposed fractional model is more accurate in the sense of MSE cost function than integer order model.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

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