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 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 Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 40 ◽  
Author(s):  
Shumaila Javeed ◽  
Dumitru Baleanu ◽  
Asif Waheed ◽  
Mansoor Shaukat Khan ◽  
Hira Affan
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Fractional Order Differential Equations ◽  
Homotopy Perturbation ◽  
The Given ◽  
Ordinary Derivative

The analysis of Homotopy Perturbation Method (HPM) for the solution of fractional partial differential equations (FPDEs) is presented. A unified convergence theorem is given. In order to validate the theory, the solution of fractional-order Burger-Poisson (FBP) equation is obtained. Furthermore, this work presents the method to find the solution of FPDEs, while the same partial differential equation (PDE) with ordinary derivative i.e., for α = 1 , is not defined in the given domain. Moreover, HPM is applied to a complicated obstacle boundary value problem (BVP) of fractional order.

scholarly journals A Modified Techniques of Fractional-Order Cauchy-Reaction Diffusion Equation via Shehu Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Mounirah Areshi ◽  
A. M. Zidan ◽  
Rasool Shah ◽  
Kamsing Nonlaopon
Keyword(s):  
Fractional Order ◽  
Reaction Diffusion ◽  
Approximate Solutions ◽  
Transformation Method ◽  
Reaction Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Closed Form Solutions ◽  
Homotopy Perturbation ◽  
In Series ◽  
The Given

In this article, the iterative transformation method and homotopy perturbation transformation method are applied to calculate the solution of time-fractional Cauchy-reaction diffusion equations. In this technique, Shehu transformation is combined of the iteration and the homotopy perturbation techniques. Four examples are examined to show validation and the efficacy of the present methods. The approximate solutions achieved by the suggested methods indicate that the approach is easy to apply to the given problems. Moreover, the solution in series form has the desire rate of convergence and provides closed-form solutions. It is noted that the procedure can be modified in other directions of fractional order problems. These solutions show that the current technique is very straightforward and helpful to perform in applied sciences.

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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