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On Analytical Approximate Solution of the Fractional Type Rosenau-Hyman Equation

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Języki publikacji
EN
Abstrakty
EN
In this paper, an approximate solution of the fractional type Rosenau-Hyman equation according to an appropriate initial condition will be obtained with the help of the reduced differential transform method (RDTM). The fractional derivatives are described in the Caputo sense. Comparing the methodology with the homotopy perturbation method and the variational iteration method will be presented. The results show that solutions obtained by the RDTM are reliable and this method is effective for this type of nonlinear fractional partial differential equations.
Wydawca
Rocznik
Strony
135--143
Opis fizyczny
Bibliogr. 27 poz., rys., tab.
Twórcy
autor
  • Department of Mathematics, University of Mazandaran, Babolsar, Iran
Bibliografia
  • [1] Podlubny I. Fractional Diferential Equations. Mathematics in Science and Engineering, Academic Press, San Diego, USA. 1999; 198. ISBN 0125588402.
  • [2] Debnath L, Bhatta D. Solutions to few linear fractional inhomogeneous partial differential equations in fluid mechanics, Fractional Calculus and Applied Analysis. 2004; 7: 153-192.
  • [3] Liu F, Burrage K. Novel techniques in parameter estimation for fractional dynamical models arising from biological systems, Math. Comput. Appl.. 2011; 62 (3): 822-833. doi: 10.1016/j.camwa.2011.03.002.
  • [4] Yang XJ. Advanced local fractional calculus and its applications, World Science Publisher LLC. New York, NY, USA, 2012. ISBN: 1938576012, 9781938576010.
  • [5] Zhang Y, Chen S, Wang S, Yang J, Phillips P. Magnetic resonance brain image classification based on weighted-type fractional Fourier transform and nonparallel support vector machine, International Journal of Imaging Systems and Technology, 2015: 24 (4): 317-327. doi: 10.1002/ima.22144.
  • [6] Wang S, Zhang Y, Yang X, Sun P, Dong Z, Liu A, Yuan T. Pathological brain detection by a novel image feature fractional Fourier entropy, Entropy. 2015; 17 (12): 8278-8296. doi: 10.3390/e17127877.
  • [7] Zhang Y, Wang S, Ge Liu G, Yang J. Computer-aided diagnosis of abnormal breasts in mammogram images by weighted-type fractional Fourier transform., Advances in Mechanical Engineering, 2015; 8 (2): 1-11. doi: 10.1177/1687814016634243.
  • [8] Zhang Y, Yang X, Cattani C, Rao VR, Wang S, Phillips P. Tea category identification using a novel fractional Fourier entropy and Jaya algorithm. Entropy. 2016; 18 (3): 77. doi: 10.3390/e18030077.
  • [9] Yang XJ, Zhang Y. A New Adomian Decomposition Procedure Scheme for Solving Local Fractional Volterra Integral Equation, Advances in Information Technology and Management, 2012; 1 (4): 158-161. ISSN: 2167-6372.
  • [10] Molliq RY, Noorani MSM. Solving the Fractional Rosenau-Hyman Equation via Variational Iteration Method and Homotopy Perturbation Method, International Journal of Differential Equations. Article ID 472030, 2012, p. 14. doi: 10.1155/2012/472030.
  • [11] Momani S, Odibat Z. Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations, Computers and Mathematics with Applications, 2007; 54 (7-8): 910-919. doi: 10.1016/j.camwa.2006.12.037.
  • [12] Zhang Y, Srivastava HM, Baleanu MC. Local fractional variational iteration algorithm II for non-homogeneous model associated with the non-differentiable heat flow, Adv. Mech. Eng., 2015; 7 (10): 1-7. doi: 10.1177/1687814015608567.
  • [13] Jafari, H., Seifi, S.: Homotopy analysis method for solving linear and nonlinear fractional diffusion-wave equation, Communications in Nonlinear Science and Numerical Simulation, 2009; 14 (5): 2006-2012. doi: 10.1016/j.cnsns.2008.05.008.
  • [14] Gupta PK. Approximate analytical solutions of fractional Benney-Lin equation by reduced differential transform method and the homotopy perturbation method, Computer and Mathematics with Application, 2011; 58: 28-39.
  • [15] Yang XJ, Srivastava HM, Cattani C. Local fractional homotopy perturbation method for solving fractal partial differential equations arising in mathematical physics, Romanian reports in Physics. 2015; 67 (3): 752-761.
  • [16] Yang XJ, Baleanu D, Srivastava HM. Local fractional similarity solution for the diffusion equation defined on Cantor sets, Applied Mathematics letters, 2015; 47: 54-60. doi: 10.1016/j.aml.2015.02.024.
  • [17] Su WH, Yang XJ, Jafari H, Baleanu D. Fractional complex transform method for wave equations on Cantor sets within local fractional differential operator, Advances in Difference Equations, 2013; 1: 1-8. doi: 10.1186/1687-1847-2013-97.
  • [18] Yan SP. Local fractional Laplace series expansion method for diffusion equation arising in fractal heat transfer. Thermal Science, 2015; 19: 131-135. doi: 10.2298/TSCI141010063Y.
  • [19] Jafari H, Tajadodi H, Johnston SJ. A decomposition method for solving diffusion equations via local fractional time derivative. Thermal Science, 2015; 19: 123-129. doi: 10.2298/TSCI15SlS23J.
  • [20] Yang XJ, Srivastava HM, Baleanu D. Initial-boundary value problems for local fractional Laplace equation arising in fractal electrostatics, J. Appl. Nonlin. Dynam., 2015; 4: 349-356. doi: 10.5890/JAND.2015.11.002.
  • [21] Zhou JK. Differential transform and its applications for Electrical Circuits, Huazhong University Press, Wuhan, China, 1986.
  • [22] Keskin Y, Oturanc G. Reduced differential transform method for partial differential equations, Int. J. Nonlinear Sci. Numer. Simul., 2009; 10 (6): 714-749. ISSN: 15651339.
  • [23] Keskin Y, Oturanc G. Reduced Differential Transform Method for solving linear and nonlinear wave equations, Iranian. J. Sci. and Tech., Transaction A, 2010; 34 (2): 113-122.
  • [24] Momani S, Odibat Z. A generalized differential transform method for linear partial differential equations of fractional order, Applied Mathematics letters, 2008; 21: 194-199. doi: 10.1016/j.aml.2007.02.022.
  • [25] Yang XJ, Tenreiro Machado JA, Srivastava HM. A new numerical technique for solving the local fractional diffusion equation: Two-dimensional extended differential transform approach, Appl. Math. Comput., 2016; 274: 143-151. doi: 10.1016/j.amc.2015.10.072.
  • [26] Rosenau P, Hyman JM. Compactons: solitons with finite wavelength, Physical Review Letters, 1993; 70 (5): 564-567. doi: http://dx.doi.org/10.1103/PhysRevLett.70.564.
  • [27] Caputo M. Linear models of dissipation whose Q is almost frequency independent, part II. Journal of the Royal Astronomical Society, 1967; 13: 529-539. doi: 10.1111/j.1365-246X.1967.tb02303.x.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
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