Homotopi pertürbasyon Elzaki dönüşümü yöntemi ile doğrusal olmayan zaman-kesirli kısmi diferansiyel denklemler için yeni yaklaşık analitik çözümler
- 8 July 2022
- journal article
- Published by Balikesir Universitesi Fen Bilimleri Enstitusu Dergisi in Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
- Vol. 24 (2), 468-482
- https://doi.org/10.25092/baunfbed.984440
Abstract
Some nonlinear time-fractional partial differential equations are solved by homotopy perturbation Elzaki transform method. The fractional derivatives are defined in the Caputo sense. The applications are examined by homotopy perturbation Elzaki transform method. Besides, the graphs of the solutions are plotted in the MAPLE software. Also, absolute error comparison of homotopy perturbation Elzaki transform method and homotopy perturbation Sumudu transform method solutions with the exact solution of nonlinear time-fractional partial differential equations is presented. In addition, this absolute error comparison is indicated in the tables. The novelty of this article is the first analysis of both the gas dynamics equation of Caputo fractional order and the Klein-Gordon equation of Caputo fractional order via this method. Thus, homotopy perturbation Elzaki transform method is quick and effective in obtaining the analytical solutions of time-fractional partial differential equations.Keywords
This publication has 33 references indexed in Scilit:
- On nonlinear fractional Klein–Gordon equationSignal Processing, 2011
- Solitary wave solutions for the KdV and mKdV equations by differential transform methodChaos, Solitons, and Fractals, 2009
- ADDENDUM: NEW INTERPRETATION OF HOMOTOPY PERTURBATION METHODInternational Journal of Modern Physics B, 2006
- Homotopy perturbation method for solving boundary value problemsPhysics Letters A, 2006
- Solutions of the system of differential equations by differential transform methodApplied Mathematics and Computation, 2003
- Homotopy perturbation method: a new nonlinear analytical techniqueApplied Mathematics and Computation, 2003
- Space- and time-fractional diffusion and wave equations, fractional Fokker–Planck equations, and physical motivationChemical Physics, 2002
- Fractional quantum mechanicsPhysical Review E, 2000
- Variational iteration method – a kind of non-linear analytical technique: some examplesInternational Journal of Non-Linear Mechanics, 1999
- A reliable modification of Adomian decomposition methodApplied Mathematics and Computation, 1999