Some analytical and numerical investigation of a family of fractional‐order Helmholtz equations in two space dimensions

2019 ◽  
Vol 43 (1) ◽  
pp. 199-212 ◽  
Author(s):  
Hari M. Srivastava ◽  
Rasool Shah ◽  
Hassan Khan ◽  
Muhammad Arif
Keyword(s):  
Numerical Investigation ◽  
Fractional Order ◽  
Helmholtz Equations ◽  
Two Space Dimensions

scholarly journals An efficient approach for solution of fractional-order Helmholtz equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nehad Ali Shah ◽  
Essam R. El-Zahar ◽  
Mona D. Aljoufi ◽  
Jae Dong Chung
Keyword(s):  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Hybrid Technique ◽  
Science And Engineering ◽  
Helmholtz Equations ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Suggested Technique ◽  
Present Technique

AbstractIn this article, a hybrid technique called the homotopy perturbation Elzaki transform method has been implemented to solve fractional-order Helmholtz equations. In the hybrid technique, the Elzaki transform method and the homotopy perturbation method are amalgamated. Three problems are solved to validate and demonstrate the efficacy of the present technique. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the results by other techniques. It is shown that the proposed method is efficient, reliable and easy to implement for various related problems of science and engineering.

Modeling and numerical investigation of fractional‐order bovine babesiosis disease

2020 ◽  
Author(s):  
Aqeel Ahmad ◽  
Muhammad Farman ◽  
Parvaiz Ahmad Naik ◽  
Nayab Zafar ◽  
Ali Akgul ◽  
...  
Keyword(s):  
Numerical Investigation ◽  
Fractional Order ◽  
Bovine Babesiosis

Numerical investigation for handling fractional-order Rabinovich–Fabrikant model using the multistep approach

2016 ◽  
Vol 22 (3) ◽  
pp. 773-782 ◽  
Author(s):  
Khaled Moaddy ◽  
Asad Freihat ◽  
Mohammed Al-Smadi ◽  
Eman Abuteen ◽  
Ishak Hashim
Keyword(s):  
Numerical Investigation ◽  
Fractional Order

scholarly journals Application of Asymptotic Homotopy Perturbation Method to Fractional Order Partial Differential Equation

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2215
Author(s):  
Haji Gul ◽  
Sajjad Ali ◽  
Kamal Shah ◽  
Shakoor Muhammad ◽  
Thanin Sitthiwirattham ◽  
...  
Keyword(s):  
Perturbation Method ◽  
Fractional Order ◽  
Homotopy Perturbation Method ◽  
Approximate Solutions ◽  
Order Partial Differential Equation ◽  
Two Dimensional ◽  
Numerical Treatment ◽  
Helmholtz Equations ◽  
Homotopy Perturbation ◽  
Linear Differential

In this article, we introduce a new algorithm-based scheme titled asymptotic homotopy perturbation method (AHPM) for simulation purposes of non-linear and linear differential equations of non-integer and integer orders. AHPM is extended for numerical treatment to the approximate solution of one of the important fractional-order two-dimensional Helmholtz equations and some of its cases . For probation and illustrative purposes, we have compared the AHPM solutions to the solutions from another existing method as well as the exact solutions of the considered problems. Moreover, it is observed that the symmetry or asymmetry of the solution of considered problems is invariant under the homotopy definition. Error estimates for solutions are also provided. The approximate solutions of AHPM are tabulated and plotted, which indicates that AHPM is effective and explicit.

scholarly journals Numerical investigation of fractional-order unsteady natural convective radiating flow of nanofluid in a vertical channel

2019 ◽  
Vol 4 (5) ◽  
pp. 1416-1429 ◽  
Author(s):  
Muhammad Hamid ◽  
◽  
Tamour Zubair ◽  
Muhammad Usman ◽  
Rizwan Ul Huq ◽  
...  
Keyword(s):  
Numerical Investigation ◽  
Fractional Order ◽  
Vertical Channel

scholarly journals The Analysis of Fractional-Order Helmholtz Equations via a Novel Approach

2021 ◽  
Author(s):  
Pongsakorn Sunthrayuth ◽  
Zeyad Al-Zhour ◽  
Yu-Ming Chu
Keyword(s):  
Fractional Order ◽  
Present Method ◽  
Computational Cost ◽  
Analytical Techniques ◽  
Form Solution ◽  
Effective Technique ◽  
Helmholtz Equations ◽  
Inverse Transform ◽  
Novel Approach ◽  
Fractional Analysis

This paper is related to the fractional view analysis of Helmholtz equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of Caputo-operator sense. In the current methodology, first, we applied the r-Laplace transform to the targeted problem. The iterative method is then implemented to obtain the series form solution. After using the inverse transform of the r-Laplace, the desire analytical solution is achieved. The suggested procedure is verified through specific examples of the fractional Helmholtz equations. The present method is found to be an effective technique having a closed resemblance with the actual solutions. The proposed technique has less computational cost and a higher rate of convergence. The suggested methods are therefore very useful to solve other systems of fractional order problems.

scholarly journals Numerical Investigation of Fractional-Order Swift–Hohenberg Equations via a Novel Transform

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1263
Author(s):  
Kamsing Nonlaopon ◽  
Abdullah M. Alsharif ◽  
Ahmed M. Zidan ◽  
Adnan Khan ◽  
Yasser S. Hamed ◽  
...  
Keyword(s):  
Fluid Dynamics ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Derivative ◽  
Numerical Investigation ◽  
Fractional Order ◽  
Thermal Convection ◽  
Formation Process ◽  
Decomposition Method ◽  
Numerical Examples

In this paper, the Elzaki transform decomposition method is implemented to solve the time-fractional Swift–Hohenberg equations. The presented model is related to the temperature and thermal convection of fluid dynamics, which can also be used to explain the formation process in liquid surfaces bounded along a horizontally well-conducting boundary. In the Caputo manner, the fractional derivative is described. The suggested method is easy to implement and needs a small number of calculations. The validity of the presented method is confirmed from the numerical examples. Illustrative figures are used to derive and verify the supporting analytical schemes for fractional-order of the proposed problems. It has been confirmed that the proposed method can be easily extended for the solution of other linear and non-linear fractional-order partial differential equations.

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