scholarly journals Numerical Investigation of the Time-Fractional Whitham–Broer–Kaup Equation Involving without Singular Kernel Operators

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Kamsing Nonlaopon ◽  
Muhammad Naeem ◽  
Ahmed M. Zidan ◽  
Rasool Shah ◽  
Ahmed Alsanad ◽  
...  
Keyword(s):  
Fractional Order ◽  
Real World ◽  
Analytical Method ◽  
Laplace Transformation ◽  
Fractional Derivatives ◽  
Perturbation Technique ◽  
Homotopy Perturbation ◽  
Real World Problem ◽  
Kernel Operators ◽  
Homotopy Perturbation Technique

This paper aims to implement an analytical method, known as the Laplace homotopy perturbation transform technique, for the result of fractional-order Whitham–Broer–Kaup equations. The technique is a mixture of the Laplace transformation and homotopy perturbation technique. Fractional derivatives with Mittag-Leffler and exponential laws in sense of Caputo are considered. Moreover, this paper aims to show the Whitham–Broer–Kaup equations with both derivatives to see their difference in a real-world problem. The efficiency of both operators is confirmed by the outcome of the actual results of the Whitham–Broer–Kaup equations. Some problems have been presented to compare the solutions achieved with both fractional-order derivatives.

scholarly journals An Analytical View of Fractional-Order Fisher’s Type Equations within Caputo Operator

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Nehad Ali Shah
Keyword(s):  
Applied Sciences ◽  
Fractional Order ◽  
Perturbation Technique ◽  
Analytical Investigation ◽  
Homotopy Perturbation ◽  
Research Article ◽  
The Given ◽  
Homotopy Perturbation Technique

The present research article is related to the analytical investigation of some nonlinear fractional-order Fisher’s equations. The homotopy perturbation technique and Shehu transformation are implemented to discuss the fractional view analysis of Fisher’s equations. For a better understanding of the proposed procedure, some examples related to Fisher’s equations are presented. The identical behavior of the derived and actual solutions is observed. The solutions at different fractional are calculated, which describe some useful dynamics of the given problems. The proposed technique can be modified to study the fractional view analysis of other problems in various areas of applied sciences.

scholarly journals Numerical Investigation of Time-Fractional Equivalent Width Equations that Describe Hydromagnetic Waves

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 418
Author(s):  
Nehad Ali Shah ◽  
Ioannis Dassios ◽  
Jae Dong Chung
Keyword(s):  
Applied Sciences ◽  
Numerical Investigation ◽  
Fractional Order ◽  
Equivalent Width ◽  
Perturbation Technique ◽  
Analytical Investigation ◽  
Homotopy Perturbation ◽  
Research Article ◽  
Hydromagnetic Waves ◽  
Homotopy Perturbation Technique

The present research article is related to the analytical investigation of some fractional-order equal-width equations. The homotopy perturbation technique along with Elzaki transformation is implemented to discuss the fractional view analysis of equal-width equations. For better understanding of the proposed procedure some examples related to equal-width equations are presented. The identical behavior of the derived and actual solutions is observed. The proposed technique can be modified to study the fractional view analysis of other problems in various areas of applied sciences.

scholarly journals A Mathematical Model to Solve the Burgers-Huxley Equation by using New Homotopy Perturbation Method

2019 ◽  
Vol 4 (6) ◽  
pp. 1483-1495
Author(s):  
Dinesh Kumar Maurya ◽  
Ravendra Singh ◽  
Yogendra Kumar Rajoria
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Perturbation Method ◽  
Real World ◽  
Analytical Method ◽  
Homotopy Perturbation Method ◽  
Three Dimension ◽  
Homotopy Perturbation ◽  
Precise Solution ◽  
Huxley Equation

A semi-analytical method has been planned for the precise solution of the differential equation established on the New Homotopy Perturbation Method (NHPM), and to develop a generalized Burger-Huxley (BH) equation, in this paper. By employing NHPM, two case studies show the precise solution of the BH equation. It is shown that the NHPM is yield solution is convergent from with the easy computability term; NHPM is an effective and easy tool for cracking many real world difficulties. The three-dimension and two dimension graphical solutions of the BH equations are also provided to validate the mathematical models. MATLAB software is used to calculate the series obtained from HPM.

scholarly journals Analysis of the Time Fractional-Order Coupled Burgers Equations with Non-Singular Kernel Operators

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2326
Author(s):  
Noufe H. Aljahdaly ◽  
Ravi P. Agarwal ◽  
Rasool Shah ◽  
Thongchai Botmart
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Burgers Equation ◽  
Singular Kernel ◽  
Exact Results ◽  
Burgers Equations ◽  
Kernel Operators ◽  
Natural Decomposition

In this article, we have investigated the fractional-order Burgers equation via Natural decomposition method with nonsingular kernel derivatives. The two types of fractional derivatives are used in the article of Caputo–Fabrizio and Atangana–Baleanu derivative. We employed Natural transform on fractional-order Burgers equation followed by inverse Natural transform, to achieve the result of the equations. To validate the method, we have considered a two examples and compared with the exact results.

scholarly journals Image Reconstruction Based on Homotopy Perturbation Inversion Method for Electrical Impedance Tomography

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jing Wang ◽  
Bo Han
Keyword(s):  
Image Reconstruction ◽  
Electrical Impedance Tomography ◽  
Electrical Impedance ◽  
Perturbation Technique ◽  
Inversion Method ◽  
Impedance Tomography ◽  
Data Noise ◽  
Homotopy Perturbation ◽  
Ill Posed ◽  
Homotopy Perturbation Technique

The image reconstruction for electrical impedance tomography (EIT) mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.

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