THERMAL SCIENCE

International Scientific Journal

Hajira Irshad

,

Mehnaz Shakeel

,

Imtiaz AhmadORCID

,

Hijaz Ahmad

,

Chutarat Tearnbucha

,

Weerawat Sudsutad

SIMULATION OF GENERALIZED TIME FRACTIONAL GARDNER EQUATION UTILIZING IN PLASMA PHYSICS FOR NON-LINEAR PROPAGATION OF ION-ACOUSTIC WAVES

ABSTRACT
In this work, radial basis function collocation method (RBFCM) is implemented for generalized time fractional Gardner equation (GTFGE). The RBFCM is meshless and easy-to-implement in complex geometries and higher dimensions, therefore, it is highly demanding. In this work, the Caputo derivative of fractional order ξ ∈ (0, 1] is used to approximate the first order time derivative whereas, Crank-Nicolson scheme is hired to approximate space derivatives. The numerical solutions are presented and discussed, which demonstrate that the method is effective and accurate.
KEYWORDS
radial basis functions, time fractional Gardner equation, time fractional derivative
PAPER SUBMITTED: 2022-02-10
PAPER REVISED: 2022-03-04
PAPER ACCEPTED: 2022-03-14
PUBLISHED ONLINE: 2023-04-08
DOI REFERENCE: https://doi.org/10.2298/TSCI23S1121I
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Special Issue, PAGES [121 - 128]
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Simulation of generalized time fractional Gardner equation utilizing in plasma physics for non-linear propagation of ion-acoustic waves

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence