scholarly journals Computing bifurcations behavior of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types in hilbert space with error analysis

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3845-3853 ◽  
Author(s):  
Banan Maayah ◽  
Feras Yousef ◽  
Omar Arqub ◽  
Shaher Momani ◽  
Ahmed Alsaedi
Keyword(s):  
Present Method ◽  
Mixed Type ◽  
Numerical Solutions ◽  
Integrodifferential Equations ◽  
Computational Method ◽  
Function Type ◽  
Fractional Equations ◽  
Singular Integrodifferential Equations ◽  
Linear And Nonlinear ◽  
Singular Time

In this article, we propose and analyze a computational method for the numerical solutions of mixed type singular time-fractional partial integrodifferential equations of Dirichlet functions types. The method provide appropriate representation of the solutions in infinite series formula with accurately computable structures. By interrupting the n-term of exact solutions, numerical solutions of linear and nonlinear singular time-fractional equations of nonhomogeneous function type are studied from mathematical viewpoint. The utilized results show that the present method and simulated annealing provide a good scheduling methodology to such singular integrodifferential equations.

scholarly journals A Note on Double Conformable Laplace Transform Method and Singular One Dimensional Conformable Pseudohyperbolic Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 949 ◽  
Author(s):  
Hassan Eltayeb ◽  
Said Mesloub ◽  
Yahya T. Abdalla ◽  
Adem Kılıçman
Keyword(s):  
Present Method ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
High Accuracy ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Numerical Examples ◽  
One Dimensional ◽  
Linear And Nonlinear ◽  
Laplace Decomposition Method

The purpose of this article is to obtain the exact and approximate numerical solutions of linear and nonlinear singular conformable pseudohyperbolic equations and conformable coupled pseudohyperbolic equations through the conformable double Laplace decomposition method. Further, the numerical examples were provided in order to demonstrate the efficiency, high accuracy, and the simplicity of present method.

scholarly journals A New Coupled Fractional Reduced Differential Transform Method for the Numerical Solutions of(2+1)-Dimensional Time Fractional Coupled Burger Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
S. Saha Ray
Keyword(s):  
Approximate Solution ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Present Method ◽  
Fractional Derivatives ◽  
Numerical Solutions ◽  
Transform Method ◽  
Differential Transform ◽  
Fractional Differential ◽  
Linear And Nonlinear

A very new technique, coupled fractional reduced differential transform, has been implemented to obtain the numerical approximate solution of (2 + 1)-dimensional coupled time fractional burger equations. The fractional derivatives are described in the Caputo sense. By using the present method we can solve many linear and nonlinear coupled fractional differential equations. The obtained results are compared with the exact solutions. Numerical solutions are presented graphically to show the reliability and efficiency of the method.

DFT based computational methodology of IC50 prediction

2020 ◽  
Vol 16 ◽  
Author(s):  
Arijit Bag
Keyword(s):  
Present Method ◽  
Dipole Moments ◽  
Research Work ◽  
Organometallic Compounds ◽  
Computational Method ◽  
Unknown Compound ◽  
Drug Designing ◽  
Further Development ◽  
Similar Kind ◽  
Hiv 1

Background: IC50 is one of the most important parameters of a drug. But, it is very difficult to predict this value of a new compound without experiment. There are only a few QSAR based methods available for IC50 prediction which is also highly dependable on huge number of known data. Thus, there is an immense demand for a sophisticated computational method of IC50 prediction, in the field of in-silico drug designing. Objective: Recently developed quantum computation based method of IC50 prediction by Bag and Ghorai requires an affordable known data. In present research work further development of this method is carried out such that the requisite number of known data being minimal. Methods: To retrench the cardinal data span and shrink the effects of variant biological parameters on the computed value of IC50, a relative approach of IC50 computation is pursued in the present method. To predict an approximate value of IC50 of a small molecule, only the IC50 of a similar kind of molecule is required for this method. Results: The present method of IC50 computation is tested for both organic and organometallic compounds as HIV-1 capsid A inhibitor and cancer drugs. Computed results match very well with the experiment. Conclusion: This method is easily applicable to both organic and organometallic com- pounds with acceptable accuracy. Since this method requires only the dipole moments of an unknown compound and the reference compound, IC50 based drug search is possible with this method. An algorithm is proposed here for IC50 based drug search.

scholarly journals System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 787
Author(s):  
Olaniyi Iyiola ◽  
Bismark Oduro ◽  
Trevor Zabilowicz ◽  
Bose Iyiola ◽  
Daniel Kenes
Keyword(s):  
Fractional Order ◽  
Recovery Rate ◽  
Death Rate ◽  
Numerical Solutions ◽  
Complex Nature ◽  
Uniqueness Of Solutions ◽  
Fractional Equations ◽  
Effective Contact ◽  
Proposed Model ◽  
Fractional Models

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.

scholarly journals A Pseudospectral Algorithm for Solving Multipantograph Delay Systems on a Semi-Infinite Interval Using Legendre Rational Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
E. H. Doha ◽  
D. Baleanu ◽  
A. H. Bhrawy ◽  
R. M. Hafez
Keyword(s):  
Numerical Solutions ◽  
Rational Functions ◽  
Absolute Error ◽  
Delay Systems ◽  
Infinite Interval ◽  
Algebraic Equations ◽  
Collocation Points ◽  
Nonlinear Algebraic Equations ◽  
Linear And Nonlinear ◽  
Pseudospectral Scheme

A new Legendre rational pseudospectral scheme is proposed and developed for solving numerically systems of linear and nonlinear multipantograph equations on a semi-infinite interval. A Legendre rational collocation method based on Legendre rational-Gauss quadrature points is utilized to reduce the solution of such systems to systems of linear and nonlinear algebraic equations. In addition, accurate approximations are achieved by selecting few Legendre rational-Gauss collocation points. The numerical results obtained by this method have been compared with various exact solutions in order to demonstrate the accuracy and efficiency of the proposed method. Indeed, for relatively limited nodes used, the absolute error in our numerical solutions is sufficiently small.

scholarly journals Modified Variational Iteration Algorithm-II: Convergence and Applications to Diffusion Models

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-14 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu ◽  
Imtiaz Ahmad
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Nonlinear Models ◽  
Nonlinear Differential Equations ◽  
Variational Iteration Method ◽  
Iteration Algorithm ◽  
Compact Finite Difference Method ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
The Stability

Variational iteration method has been extensively employed to deal with linear and nonlinear differential equations of integer and fractional order. The key property of the technique is its ability and flexibility to investigate linear and nonlinear models conveniently and accurately. The current study presents an improved algorithm to the variational iteration algorithm-II (VIA-II) for the numerical treatment of diffusion as well as convection-diffusion equations. This newly introduced modification is termed as the modified variational iteration algorithm-II (MVIA-II). The convergence of the MVIA-II is studied in the case of solving nonlinear equations. The main advantage of the MVIA-II improvement is an auxiliary parameter which makes sure a fast convergence of the standard VIA-II iteration algorithm. In order to verify the stability, accuracy, and computational speed of the method, the obtained solutions are compared numerically and graphically with the exact ones as well as with the results obtained by the previously proposed compact finite difference method and second kind Chebyshev wavelets. The comparison revealed that the modified version yields accurate results, converges rapidly, and offers better robustness in comparison with other methods used in the literature. Moreover, the basic idea depicted in this study is relied upon the possibility of the MVIA-II being utilized to handle nonlinear differential equations that arise in different fields of physical and biological sciences. A strong motivation for such applications is the fact that any discretization, transformation, or any assumptions are not required for this proposed algorithm in finding appropriate numerical solutions.

An Improved Element-Free Method for Compressing Cylindric Tube

2010 ◽  
Vol 145 ◽  
pp. 302-306
Author(s):  
Jian Hua Hu ◽  
Yuan Hua Shuang ◽  
Xiao Cheng Yang
Keyword(s):  
Present Method ◽  
Numerical Solutions ◽  
Essential Boundary Condition ◽  
Mesh Free ◽  
Good Accordance ◽  
Mesh Free Method ◽  
Integral Scheme ◽  
Element Free Method ◽  
Element Free ◽  
Computational Properties

In this paper, a description about improved element free Gerlink method (EFGM) is given. The method adopted penalty method to implement the essential boundary condition. The integral scheme takes Gauss background integration. Based on compressing the cylindric tube, the numerical model is calculated by finite element method (FEM) and EFGM. Comparisons of the deformation shape and stress of the both simulations showed good accordance. The numerical solutions show that the present method is a robust, reliable, stable mesh free method and possesses better computational properties compared with traditional FEM.

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