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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.

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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 -

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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.