Analytical Investigation of Nonlinear Fractional Harry Dym and Rosenau-Hyman Equation via a Novel Transform

We use a new integral transform approach to solve the fractional Harry Dym equation and fractional Rosenau-Hyman equation in this work. The Elzaki transform and the integral transformation are combined in the suggested method (ET). To handle two nonlinear problems, we first construct the Elzaki tran...

Full description

Saved in:
Bibliographic Details
Published in:Journal of function spaces 2022, Vol.2022, p.1-12
Main Authors: Alshammari, Saleh, Iqbal, Naveed, Yar, Mohammad
Format: Article
Language:English
Subjects:
Calculus
Control theory
Convergence
Decomposition
Differential equations
Error analysis
Exact solutions
Fractional calculus
Integral transforms
Mathematical analysis
Partial differential equations
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We use a new integral transform approach to solve the fractional Harry Dym equation and fractional Rosenau-Hyman equation in this work. The Elzaki transform and the integral transformation are combined in the suggested method (ET). To handle two nonlinear problems, we first construct the Elzaki transforms of the Caputo fractional derivative (CFD) and Atangana-Baleanu fractional derivative (ABFD). The ultimate purpose of this study is to find an error analysis that demonstrates that our final result converges to the exact and approximate result. The convergent series form solution demonstrates the method’s efficiency in resolving several types of fractional differential equations. Furthermore, the solutions obtained in this study agree well with the exact solutions; thus, this strategy is powerful and efficient as an alternate way for obtaining approximate solutions to both linear and nonlinear fractional differential equations.
ISSN:2314-8896
2314-8888
DOI:10.1155/2022/8736030