scholarly journals An efficient hybrid technique for the solution of fractional-order partial differential equations

2021 ◽  
Vol 13 (3) ◽  
pp. 790-804
Author(s):  
H.K. Jassim ◽  
H. Ahmad ◽  
A. Shamaoon ◽  
C. Cesarano
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Order ◽  
Hybrid Technique ◽  
Science And Engineering ◽  
Partial Differential ◽  
Transform Method ◽  
Suggested Technique ◽  
Homotopy Analysis ◽  
Sumudu Transform

In this paper, a hybrid technique called the homotopy analysis Sumudu transform method has been implemented solve fractional-order partial differential equations. This technique is the amalgamation of Sumudu transform method and the homotopy analysis method. Three examples are considered to validate and demonstrate the efficacy and accuracy of the present technique. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the exact solution which shows that the proposed method is efficient, reliable and easy to implement for various related problems of science and engineering.

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.

scholarly journals Semi-Analytic Technique for Solving Fractional Partial Differential Equations with Conformable Derivatives

2021 ◽  
Vol 24 (1) ◽  
pp. 39-44
Author(s):  
Noor I. Ibrahim ◽  
◽  
Osama H. Mohammed ◽  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Approximate Methods ◽  
Analytical Technique ◽  
Suggested Technique ◽  
Homotopy Analysis ◽  
Conformable Derivatives ◽  
Approximate Result

In this work, we present a semi-analytical technique to find an approximate result of the conformable fractional partial differential equations (CFPDEs). The fractional order derivative will be in the conformable (CFD) sense. This definition is effective and simple in the solution of the fractional differential equations that have intricate solution with classical fractional derivative definition like Riemann-Liouville and Caputo. Furthermore, the result obtained by the proposed technique is like those in previous studies that used other types of approximate methods like (Homotopy analysis method) but it has the advantage of being simpler than the rest of these methods. In addition, results demonstrate obtained the Precision and effectiveness of the suggested technique.

scholarly journals Fractional View Analysis of Acoustic Wave Equations, Using Fractional-Order Differential Equations

2020 ◽  
Vol 10 (2) ◽  
pp. 610 ◽  
Author(s):  
Izaz Ali ◽  
Hassan Khan ◽  
Rasool Shah ◽  
Dumitru Baleanu ◽  
Poom Kumam ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Acoustic Wave ◽  
Fractional Order ◽  
Wave Equations ◽  
Research Work ◽  
Analytical Techniques ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation

In the present research work, a newly developed technique which is known as variational homotopy perturbation transform method is implemented to solve fractional-order acoustic wave equations. The basic idea behind the present research work is to extend the variational homotopy perturbation method to variational homotopy perturbation transform method. The proposed scheme has confirmed, that it is an accurate and straightforward technique to solve fractional-order partial differential equations. The validity of the method is verified with the help of some illustrative examples. The obtained solutions have shown close contact with the exact solutions. Furthermore, the highest degree of accuracy has been achieved by the suggested method. In fact, the present method can be considered as one of the best analytical techniques compared to other analytical techniques to solve non-linear fractional partial differential equations.

scholarly journals Tarig Projected Differential Transform Method to solve fractional nonlinear partial differential equations

2019 ◽  
Vol 38 (3) ◽  
pp. 23-46 ◽  
Author(s):  
Morachan Bagyalakshmi ◽  
G. SaiSundarakrishnan
Keyword(s):  
Heat Transfer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Computational Efficiency ◽  
Differential Transform Method ◽  
Hybrid Technique ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Differential Transform

Recent advancement in the field of nonlinear analysis and fractional calculus help to address the rising challenges in the solution of nonlinear fractional partial differential equations. This paper presents a hybrid technique, a combination of Tarig transform and Projected Differential Transform Method (TPDTM) to solve nonlinear fractional partial differential equations. The effectiveness of the method is examined by solving three numerical examples that arise in the field of heat transfer analysis. In this proposed scheme, the solution is obtained as a convergent series and the result is used to analyze the hyper diffusive process with pre local information regarding the heat transfer for different values of fractional order. In order to validate the results, a comparative study has been carried out with the solution obtained from the two methods, the Laplace Adomian Decomposition Method (LADM) and Homotophy Pertubation Method (HPM) and the result thus observed coincided with each other. Inspite of the uniformity between the solutions, the proposed hybrid technique had to overcome the complexity of manupulation of Adomian polynomials and evaluation of integrals in LADM and HPM respectively. The methodology and the results presented in this paper clearly reveals the computational efficiency of the present method. Due to its computational efficiency, the TPDTM has the potential to be used as a novel tool not only for solving nonlinear fractional differential equations but also for analysing the prelocal information of the system.

An efficient hybrid computational technique for solving nonlinear local fractional partial differential equations arising in fractal media

2018 ◽  
Vol 7 (3) ◽  
pp. 229-235 ◽  
Author(s):  
Amit Prakash ◽  
Hardish Kaur
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Planck Equation ◽  
Computational Technique ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Transform Method ◽  
Homotopy Perturbation ◽  
Fractal Media ◽  
Sumudu Transform

AbstractIn present work, nonlinear fractional partial differential equations namely transport equation and Fokker-Planck equation involving local fractional differential operators, are investigated by means of the local fractional homotopy perturbation Sumudu transform method. The proposed method is a coupling of homotopy perturbation method with local fractional Sumudu transform and is used to describe the non-differentiable problems. Numerical simulation results are projected to show the efficiency of the proposed technique.

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