Approximate Series Solution of Non Linear Fractional Dispersive Equations Using Generalized Differential Transform Method
Deepanjan Das1
Section:Research Paper, Product Type: Journal Paper
Volume-7 ,
Issue-1 , Page no. 221-228, Jan-2019
CrossRef-DOI: https://doi.org/10.26438/ijcse/v7i1.221228
Online published on Jan 31, 2019
Copyright © Deepanjan Das . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
View this paper at Google Scholar | DPI Digital Library
How to Cite this Paper
- IEEE Citation
- MLA Citation
- APA Citation
- BibTex Citation
- RIS Citation
IEEE Style Citation: Deepanjan Das, “Approximate Series Solution of Non Linear Fractional Dispersive Equations Using Generalized Differential Transform Method,” International Journal of Computer Sciences and Engineering, Vol.7, Issue.1, pp.221-228, 2019.
MLA Style Citation: Deepanjan Das "Approximate Series Solution of Non Linear Fractional Dispersive Equations Using Generalized Differential Transform Method." International Journal of Computer Sciences and Engineering 7.1 (2019): 221-228.
APA Style Citation: Deepanjan Das, (2019). Approximate Series Solution of Non Linear Fractional Dispersive Equations Using Generalized Differential Transform Method. International Journal of Computer Sciences and Engineering, 7(1), 221-228.
BibTex Style Citation:
@article{Das_2019,
author = {Deepanjan Das},
title = {Approximate Series Solution of Non Linear Fractional Dispersive Equations Using Generalized Differential Transform Method},
journal = {International Journal of Computer Sciences and Engineering},
issue_date = {1 2019},
volume = {7},
Issue = {1},
month = {1},
year = {2019},
issn = {2347-2693},
pages = {221-228},
url = {https://www.ijcseonline.org/full_paper_view.php?paper_id=3488},
doi = {https://doi.org/10.26438/ijcse/v7i1.221228}
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
DO = {https://doi.org/10.26438/ijcse/v7i1.221228}
UR - https://www.ijcseonline.org/full_paper_view.php?paper_id=3488
TI - Approximate Series Solution of Non Linear Fractional Dispersive Equations Using Generalized Differential Transform Method
T2 - International Journal of Computer Sciences and Engineering
AU - Deepanjan Das
PY - 2019
DA - 2019/01/31
PB - IJCSE, Indore, INDIA
SP - 221-228
IS - 1
VL - 7
SN - 2347-2693
ER -
VIEWS | XML | |
529 | 310 downloads | 203 downloads |
Abstract
In the present paper, generalized differential transform method (GDTM) is used for obtaining the approximate analytic solutions of non-linear dispersive partial differential equations of fractional order. The fractional derivatives are described in the Caputo sense.
Key-Words / Index Term
Fractional differential equations; Caputo fractional derivative; Generalized Differential transform method; Analytic solution. Mathematical Subject Classification (2010) — 26A33, 34A08, 35A22, 35R11, 35C10, 74H10
References
[1] J.K.Zhou,”Differential Transformation and Its Applications for Electrical Circuits”. Huazhong University Press,Wuhan, China,1986.
[2] C.K. Chen,S.H. Ho,“Solving partial differential equations by two dimensionalDifferential transform Method”,Appl. Math. Comput.,Vol.
106,pp.171–179,1999.
[3] F.Ayaz,”Solutions of the systems of differential equations by
differential transform Method",Appl. Math. Comput.,Vol.147,
pp.547–567,2004.
[4] R.Abazari,A. Borhanifar,”Numerical study of the solution of the Burgers and coupled Burgers equations by a differential transformation method”, Comput. Math. Appl.,Vol.59,
pp.2711–2722,2010
[5] C.K.Chen,”Solving partial differantial equations by two dimensional differential transformation method”,Appl. Math. Comput.,Vol.106,pp.171–179,1999
[6] M.J.Jang,C.K.Chen,”Two-dimensional differential transformation method for partial differantial equations”,Appl. Math. Comput.,
Vol.121,pp.261–270,2001.
[7] F.Kangalgil,F.Ayaz,”Solitary wave solutions for the KDV and mKDV equations by differential transformation method”, Choas Solitons Fractals,Vol.41,pp.464–472,2009.
[8] A.Arikoglu,I.Ozkol,”Solution of difference equations by using differential transformation method”,Appl. Math. Comput.,Vol.174,pp.1216–1228,2006.
[9] S.Momani,Z. Odibat,I,Hashim,”Algorithms for nonlinear fractional partial differantial equations: A selection of numerical methods”, Topol. Method Nonlinear Anal.,Vol.31,pp.211–226,2008.
[10] A.Arikoglu,I.Ozkol,”Solution of fractional differential equations by using differential transformation Method”, Chaos Solitons Fractals,Vol.34,pp.1473–1481,2007.
[11] B.Soltanalizadeh,M.Zarebnia,”Numerical analysis of the linear and nonlinear Kuramoto-Sivashinsky equation by using Differential Transformation method”. Inter. J. Appl. Math. Mechanics,Vol.7, Issue.12,pp.63–72,2011.
[12] A.Tari,M.Y.Rahimi,S.Shahmoradb,F.Talati,”Solving a class of two-dimensional linear and nonlinear Volterra integral equations by the differential transform method”,J.Comput. Appl. Math.,Vol.228,pp.70–76,2009.
[13] D.Nazari,S.Shahmorad,”Application of the fractional differential transform method to fractional-order integro-differential equations with nonlocal boundary conditions”, J. Comput. Appl. Math.,Vol.234,pp.883–891,2010.
[14] A.Borhanifar,R.Abazari,”Exact solutions for non-linear Schr.dinger equations by differential transformation Method”, J. Appl. Math. Comput.,Vol.35,pp.37–51,2011.
[15] A.Borhanifar,R.Abazari,”Numerical study of nonlinear Schr.dinger and coupled Schr.dinger equations by differential transformation method”,OpticsCommunications,Vol.283,
pp.2026–2031,2010.
[16] S.Momani,Z.Odibat,V.S.Erturk,”Generalized differential
Transform method for solving a space- and time-fractional diffusion-wave equation”, Physics Letters. A,Vol.370,Issue.5-6,pp.379–387,2007 .
[17] Z.Odibat,S.Momani,”A generalized differential transform method for linear partial Differential equations of fractional order”, Applied Mathematics Letters, Vol.21,Issue.2,pp.194–199,2008.
[18] Z.Odibat,S.Momani,V.S.Erturk,”Generalized differential
Transform method: application to differentia equations of fractionalorder”,Applied Mathematics and Computation,
Vol.197,Issue.2,pp.467–477,2008.
[19] V.S.Erturk,S.Momanib,”On the generalized differential transform method : application to fractional integro-differential equations”,
Studies in Nonlinear Sciences,Vol.1,Issue.4,pp.118-126,2010
[20] M.Garg,P.Manohar,S.L.Kalla,”Generalized differential transform method to Space-time fractional telegraph Equation”,Int.J.of
Differential Equations,Hindawi Publishing Corporation,2011,
article id.:548982,9 pages,doi.:10.1155/2011/548982.
[21] M.K.Bansal,R.Jain,”Application of generalized differential transform method to fractional order Riccati differential equation
and numerical results”,Int. J.of Pure and Appl. Math.,Vol.99,
Issue.3,pp.355-366,2015.
[22] A.Cetinkaya,O.Kiymaz,J.Camli,”Solution of non linear PDE’s of fractional order with generalized differential transform method”,
Int. Mathematical Forum,Vol.6,Issue.1,pp.39-47,2011.
[23] S.Das,”Functional Fractional Calculus”, Springer,2008.
[24] K.S.Miller,B.Ross,”An Introduction to the Fractional Calculus and Fractional Diff. Equations”, John Wiley and Son,1993.
[25] M.Caputo,”Linear models of dissipation whose q is almost frequency independent-ii”, Geophys J. R. Astron. Soc,Vol.13,
pp.529-539,1967.
[26] I,Podlubny,”Fractional differential equations: An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications”,Academic
Press,1999.
[27] R.Almeida,D.F.Torres,”Necessary and sufficient conditions for the fractional calculus of variations with caputo derivatives”,
Communications in Nonlinear Science and Numerical Simulation,
Vol.16,pp.1490-1500,2011.
[28] A.M.WazWaz,”Partial differential equations methods and applications”,Saint Xavier University,Chicago, Illinois,
USA,2002.