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      The generalized time fractional Gardner equation via numerical meshless collocation method

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          Abstract

          In this study, the meshless collocation approach is used to determine the numerical solution the generalized time-fractional Gardner equation. The Crank-Nicolson technique is used to approximate space derivatives, whereas the Caputo derivative of fractional order is used to approximate the first order time fractional derivative. The numerical solutions, which show the method?s efficacy and accuracy, are pro?vided and discussed. The numerical solution shows that our method is effective in producing extremely accurate results.

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          Linear Models of Dissipation whose Q is almost Frequency Independent--II

          Joshua Caputo (1967)
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            Application of local meshless method for the solution of two term time fractional-order multi-dimensional PDE arising in heat and mass transfer

            Imtiaz Ahmad, Hijaz Ahmad, Mustafa Inc … (2020)
            In this article, we presented an efficient local meshless method for the numerical treatment of two term time fractional-order multi-dimensional diffusion PDE. The demand of meshless techniques increment because of its meshless nature and simplicity of usage in higher dimensions. This technique approximates the solu?tion on set of uniform and scattered nodes. The space derivatives of the models are discretized by the proposed meshless procedure though the time fractional part is discretized by Liouville-Caputo fractional derivative. The numerical re?sults are obtained for 1-, 2- and 3-D cases on rectangular and non-rectangular computational domains which verify the validity, efficiency and accuracy of the method.
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              Time-fractional Gardner equation for ion-acoustic waves in negative-ion-beam plasma with negative ions and nonthermal nonextensive electrons

              Liquan Mei, Zhengqiang Zhang, Shimin Guo (2015)
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                Author and article information

                Journal
                Title: Thermal Science
                Abbreviated Title: Therm sci
                Abbreviated Title: THERM SCI
                Abbreviated Title: THERMAL SCI
                Publisher: National Library of Serbia
                ISSN (Print): 0354-9836
                ISSN (Electronic): 2334-7163
                Publication date Created: 2022
                Publication date (Print): 2022
                Volume: 26
                Issue: Spec. issue 1
                Pages: 469-474
                Affiliations
                [1 ]Department of Mathematics, Shaheed Benazir Bhutto Women University, Peshawar, Pakistan
                [2 ]Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan
                [3 ]Department of Mathematics, University of Swabi, Khyber Pakhtunkhwa, Pakistan
                [4 ]Department of Mathematics, College of Science, Taif University, Taif, Saudi Arabia
                [5 ]Department of Software Engineering, College of Computer Science and Engineering, University of Jeddah, Jeddah, Saudi Arabia
                [6 ]Firat University, Science Faculty, Department of Mathematics, Elazig, Turkiye + Department of Medical Research, China Medical University,Taichung, Taiwan
                Article
                DOI: 10.2298/TSCI22S1469M
                SO-VID: 6b8e5e84-54fe-4e79-81a7-cc39a3ae522a
                Copyright © © 2022
                License:

                http://creativecommons.org/licenses/by-nc-nd/4.0/

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