Comparison of two reliable methods to solve fractional Rosenau‐Hyman equation

In this study, we examine the numerical solutions of the time‐fractional Rosenau‐Hyman equation, which is a KdV‐like model. This model demonstrates the formation of patterns in liquid drops. For this purpose, two reliable methods, residual power series method (RPSM) and perturbation‐iteration algori...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 44; no. 10; pp. 7904 - 7914
Main Authors: Senol, Mehmet, Tasbozan, Orkun, Kurt, Ali
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 15.07.2021
Subjects:
Caputo fractional derivative
Differential equations
Drops (liquids)
Exact solutions
fractional partial differential equations
Iterative algorithms
Iterative methods
Mathematical models
Perturbation
perturbation‐iteration algorithm
Power series
residual power series method
ISSN:0170-4214, 1099-1476
Online Access:Get full text
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Summary:In this study, we examine the numerical solutions of the time‐fractional Rosenau‐Hyman equation, which is a KdV‐like model. This model demonstrates the formation of patterns in liquid drops. For this purpose, two reliable methods, residual power series method (RPSM) and perturbation‐iteration algorithm (PIA), are used to obtain approximate solutions of the model. The fractional derivative is taken in the Caputo sense. Obtained results are compared with each other and the exact solutions both numerically and graphically. The outcome shows that both methods are easy to implement, powerful, and reliable. So they are ready to implement for a variety of partial fractional differential equations.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.5497