scholarly journals An Analytical Technique Implemented in the Fractional Clannish Random Walker’s Parabolic Equation with Nonlinear Physical Phenomena

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 801
Author(s):  
Md. Nur Alam ◽  
Imran Talib ◽  
Omar Bazighifan ◽  
Dimplekumar N. Chalishajar ◽  
Barakah Almarri
Keyword(s):  
Parabolic Equation ◽  
Mathematical Models ◽  
Exact Solutions ◽  
Analytical Technique ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena ◽  
Expansion Scheme

In this paper, the adapted (G’/G)-expansion scheme is executed to obtain exact solutions to the fractional Clannish Random Walker’s Parabolic (FCRWP) equation. Some innovative results of the FCRWP equation are gained via the scheme. A diverse variety of exact outcomes are obtained. The proposed procedure could also be used to acquire exact solutions for other nonlinear fractional mathematical models (NLFMMs).

scholarly journals Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

2018 ◽  
Vol 6 (06) ◽  
Author(s):  
Figen Kangalgil
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

The investigation of the exact solutions of NLPDEs plays an im- portant role for the understanding of most nonlinear physical phenomena. Also, the exact solutions of this equations aid the numerical solvers to assess the correctness of their results. In this paper, (G'/G)-expansion method is pre- sented to construct exact solutions of the Perturbed Wadati-Segur-Ablowitz equation. Obtained the exact solutions are expressed by the hyperbolic, the trigonometric and the rational functions. All calculations have been made with the aid of Maple program. It is shown that the proposed algorithm is elemen- tary, e¤ective and has been used for many PDEs in mathematical physics.  

scholarly journals Analysis of optical solitons solutions of two nonlinear models using analytical technique

2021 ◽  
Vol 6 (12) ◽  
pp. 13258-13271
Author(s):  
Naeem Ullah ◽  
◽  
Muhammad Imran Asjad ◽  
Azhar Iqbal ◽  
Hamood Ur Rehman ◽  
...  
Keyword(s):  
Nonlinear Models ◽  
Nonlinear Partial Differential Equations ◽  
Optical Solitons ◽  
Nonlinear Dynamical ◽  
Analytical Technique ◽  
The Core ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

<abstract><p>Looking for the exact solutions in the form of optical solitons of nonlinear partial differential equations has become very famous to analyze the core structures of physical phenomena. In this paper, we have constructed some various type of optical solitons solutions for the Kaup-Newell equation (KNE) and Biswas-Arshad equation (BAE) via the generalized Kudryashov method (GKM). The conquered solutions help to understand the dynamic behavior of different physical phenomena. These solutions are specific, novel, correct and may be beneficial for edifying precise nonlinear physical phenomena in nonlinear dynamical schemes. Graphical recreations for some of the acquired solutions are offered.</p></abstract>

scholarly journals APPLICATION OF ABOODH TRANSFORM ON SOME FRACTIONAL ORDER MATHEMATICAL MODELS

2020 ◽  
Vol 20 (3) ◽  
pp. 661-672
Author(s):  
JAWARIA TARIQ ◽  
JAMSHAD AHMAD
Keyword(s):  
Mathematical Models ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Iteration Method ◽  
Analytical Techniques ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Physical Phenomena ◽  
Convergent Solution

In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.

scholarly journals LabVIEW Interface for Controlling a Test Bench for Photovoltaic Modules and Extraction of Various Parameters

2015 ◽  
Vol 6 (3) ◽  
pp. 498 ◽  
Author(s):  
Abderrezak Guenounou ◽  
Ali Malek ◽  
Michel Aillerie ◽  
Achour Mahrane
Keyword(s):  
Numerical Simulation ◽  
Mathematical Models ◽  
Energy Production ◽  
Test Bench ◽  
Graphical Interface ◽  
Detailed Report ◽  
Photovoltaic Modules ◽  
Pv Modules ◽  
Computer Controlled ◽  
Physical Phenomena

Numerical simulation using mathematical models that take into account physical phenomena governing the operation of solar cells is a powerful tool to predict the energy production of photovoltaic modules prior to installation in a given site. These models require some parameters that manufacturers do not generally give. In addition, the availability of a tool for the control and the monitoring of performances of PV modules is of great importance for researchers, manufacturers and distributors of PV solutions. In this paper, a test and characterization protocol of PV modules is presented. It consists of an outdoor computer controlled test bench using a LabVIEW graphical interface. In addition to the measuring of the IV characteristics, it provides all the parameters of PV modules with the possibility to display and print a detailed report for each test. After the presentation of the test bench and the developed graphical interface, the obtained results based on an experimental example are presented.

scholarly journals A Novel Analytical Technique to Obtain Kink Solutions for Higher Order Nonlinear Fractional Evolution Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Qazi Mahmood Ul Hassan ◽  
Jamshad Ahmad ◽  
Muhammad Shakeel
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Fractional Derivatives ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Fractional Evolution Equations ◽  
Analytical Technique ◽  
Fractional Complex Transform ◽  
Fifth Order

We use the fractional derivatives in Caputo’s sense to construct exact solutions to fractional fifth order nonlinear evolution equations. A generalized fractional complex transform is appropriately used to convert this equation to ordinary differential equation which subsequently resulted in a number of exact solutions.

scholarly journals A Partial Lagrangian Approach to Mathematical Models of Epidemiology

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
R. Naz ◽  
I. Naeem ◽  
F. M. Mahomed
Keyword(s):  
Mathematical Models ◽  
Exact Solutions ◽  
Numerical Solutions ◽  
First Integrals ◽  
Order Equation ◽  
Second Order ◽  
Lagrangian Approach ◽  
Hiv Model ◽  
First Order ◽  
Partial Lagrangian

This paper analyzes the first integrals and exact solutions of mathematical models of epidemiology via the partial Lagrangian approach by replacing the three first-order nonlinear ordinary differential equations by an equivalent system containing one second-order equation and a first-order equation. The partial Lagrangian approach is then utilized for the second-order ODE to construct the first integrals of the underlying system. We investigate the SIR and HIV models. We obtain two first integrals for the SIR model with and without demographic growth. For the HIV model without demography, five first integrals are established and two first integrals are deduced for the HIV model with demography. Then we utilize the derived first integrals to construct exact solutions to the models under investigation. The dynamic properties of these models are studied too. Numerical solutions are derived for SIR models by finite difference method and are compared with exact solutions.

Solitary dynamics of longitudinal wave equation arises in magneto-electro-elastic circular rod

2020 ◽  
pp. 2150086 ◽  
Author(s):  
Naila Sajid ◽  
Ghazala Akram
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Mapping Method ◽  
Integration Scheme ◽  
Auxiliary Equation ◽  
New Exact Solutions ◽  
Non Linear ◽  
Physical Phenomena

This paper examines the effectiveness of an integration scheme, which called the extended modified auxiliary equation mapping method in exactly solving a well-known non-linear longitudinal wave equation with dispersion caused by transverse Poisson’s effect arises in a magneto-electro-elastic (MEE) circular rod. Explicit new exact solutions are derived in different form such as hyperbolic, kinky, anti-kinky, dark, and singular solitons of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena.

scholarly journals Singular and Degenerate Boundary Value Problems Related to the Electricity Theory

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Maria-Magdalena Boureanu ◽  
Andaluzia Matei
Keyword(s):  
Sobolev Space ◽  
Mathematical Models ◽  
Existence And Uniqueness ◽  
Nonlinear Boundary ◽  
Weighted Sobolev Space ◽  
Nonlinear Boundary Conditions ◽  
Uniqueness Result ◽  
Physical Phenomena ◽  
Mathematical Literature ◽  
Weak Solvability

The present paper draws attention to the weak solvability of a class of singular and degenerate problems with nonlinear boundary conditions. These problems derive from the electricity theory serving as mathematical models for physical phenomena related to the anisotropic media with “perfect” insulators or “perfect” conductors points. By introducing an appropriate weighted Sobolev space to the mathematical literature, we establish an existence and uniqueness result.

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