A coupling method involving the Sumudu transform and the variational iteration method for a class of local fractional diffusion equations

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Authors
Feng Gao
 School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China.
 State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China.
H. M. Srivastava
 Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada.
 Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, P. R. China.
YaNan Gao
 School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China.
 State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China.
XiaoJun Yang
 School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China.
 State Key Laboratory for Geomechanics and Deep Underground Engineering, School of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, P. R. China.
Abstract
In this article, a coupling of the variational iteration method with the Sumudu transform via the local
fractional calculus operator is proposed for the first time. As a testing example, the exact solution for the
local fractional diffusion equation in fractal onedimensional space is obtained. The method provided an
accurate and efficient technique for solving the local fractional PDEs.
Share and Cite
ISRP Style
Feng Gao, H. M. Srivastava, YaNan Gao, XiaoJun Yang, A coupling method involving the Sumudu transform and the variational iteration method for a class of local fractional diffusion equations, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 11, 58305835
AMA Style
Gao Feng, Srivastava H. M., Gao YaNan, Yang XiaoJun, A coupling method involving the Sumudu transform and the variational iteration method for a class of local fractional diffusion equations. J. Nonlinear Sci. Appl. (2016); 9(11):58305835
Chicago/Turabian Style
Gao, Feng, Srivastava, H. M., Gao, YaNan, Yang, XiaoJun. "A coupling method involving the Sumudu transform and the variational iteration method for a class of local fractional diffusion equations." Journal of Nonlinear Sciences and Applications, 9, no. 11 (2016): 58305835
Keywords
 Diffusion equation
 exact solution
 variational iteration method
 Sumudu transform
 local fractional calculus.
MSC
References

[1]
S. Blasiak, Timefractional heat transfer equations in modeling of the noncontacting face seals, Int. J. Heat Mass Transf., 100 (2016), 7988

[2]
L. Chen, B. Basu, D. McCabe, Fractional order models for system identification of thermal dynamics of buildings, Energy and Buildings, 133 (2016), 381388

[3]
R. S. Damor, S. Kumar, A. K. Shukla, Solution of fractional bioheat equation in terms of Fox's Hfunction, SpringerPlus, 5 (2016), 10 pages

[4]
M. A. Ezzat, State space approach to thermoelectric fluid with fractional order heat transfer, Heat Mass Transf., 48 (2012), 7182

[5]
M. A. Ezzat, A. A. ElBary, Effects of variable thermal conductivity and fractional order of heat transfer on a perfect conducting infinitely long hollow cylinder, Int. J. Thermal Sci., 108 (2016), 6269

[6]
J. Hristov, Heatbalance integral to fractional (halftime) heat diffusion submodel, Thermal Sci., 14 (2010), 291316

[7]
F. Huang, F. Liu, The spacetime fractional diffusion equation with Caputo derivatives, J. Appl. Math. Comput., 19 (2005), 179190

[8]
I. S. Jesus, J. A. T. Machado, Fractional control of heat diffusion systems, Nonlinear Dyn., 54 (2008), 263282

[9]
V. V. Kulish, J. L. Large, Fractionaldiffusion solutions for transient local temperature and heat flux, ASME J. Heat Transf., 122 (2000), 372376

[10]
C.F. Liu, S.S. Kong, S.J. Yuan, Reconstructive schemes for variational iteration method within YangLaplace transform with application to fractal heat conduction problem, Thermal Sci., 17 (2013), 715721

[11]
L. Liu, L. Zheng, F. Liu, X. Zhang, An improved heat conduction model with Riesz fractional CattaneoChristov flux, Int. J. Heat Mass Transf., 103 (2016), 11911197

[12]
M. Ma, D. Baleanu,Y. S. Gasimov, X.J. Yang, New results for multidimensional diffusion equations in fractal dimensional space, Rom. J. Phys., 61 (2016), 784794

[13]
Y. Z. Povstenko, Fractional heat conduction in infinite onedimensional composite medium, J. Thermal Stresses, 36 (2013), 351363

[14]
G. S. Priya, P. Prakash, J. J. Nieto, Z. Kayar, Higherorder numerical scheme for the fractional heat equation with Dirichlet and Neumann boundary conditions, Numer. Heat Trans., Part B: Fund.: Int. J. Comput. Methodol., 63 (2013), 540559

[15]
R. Simpson, A. Jaques, H. Núñez, C. Ramirez, A. Almonacid, Fractional calculus as a mathematical tool to improve the modeling of mass transfer phenomena in food processing, Food Eng. Rev., 5 (2013), 4555

[16]
J. Singh, D. Kumar, J. J. Nieto, A reliable algorithm for a local fractional Tricomi equation arising in fractal transonic flow, Entropy, 18 (2016), 8 pages

[17]
H. M. Srivastava, A. K. Golmankhaneh, D. Baleanu, X.J. Yang, Local fractional Sumudu transform with application to IVPs on Cantor sets, Abstr. Appl. Anal., 2014 (2014), 7 pages

[18]
A. Suzuki, Y. Niibori, S. A. Fomin, V. A. Chugunov, T. Hashida, Analysis of water injection in fractured reservoirs using a fractionalderivativebased mass and heat transfer model, Math. Geosci., 47 (2015), 3149

[19]
X.J. Yang, Advanced local fractional calculus and its applications, World Science Publisher, New York (2012)

[20]
X.J. Yang, D. Baleanu, Fractal heat conduction problem solved by local fractional variation iteration method, Thermal Sci.,, 17 (2013), 625628

[21]
X.J. Yang, D. Baleanu, H. M. Srivastava, Local fractional similarity solution for the diffusion equation defined on Cantor sets, Appl. Math. Lett., 47 (2015), 5460

[22]
X.J. Yang, D. Baleanu, H. M. Srivastava, Local fractional integral transforms and their applications, Elsevier/ Academic Press, Amsterdam (2016)

[23]
X.J. Yang, H. M. Srivastava, An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives, Commun. Nonlinear Sci. Numer. Simul., 29 (2015), 499504