THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

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Ming-Feng Zhang

,

Yan-Qin Liu

,

Xiao-Shuang Zhou

EFFICIENT HOMOTOPY PERTURBATION METHOD FOR FRACTIONAL NON-LINEAR EQUATIONS USING SUMUDU TRANSFORM

ABSTRACT
In this paper, we propose an efficient modification of the homotopy perturbation method for solving fractional non-linear equations with fractional initial conditions. Sumudu transform is adopted to simplify the solution process. An example is given to illustrate the solution process and effectiveness of the method.
KEYWORDS
approximate solution, homotopy perturbation method, Sumudu transform, Jumaries modified R-L fractional derivative
PAPER SUBMITTED: 2014-11-26
PAPER REVISED: 2015-03-10
PAPER ACCEPTED: 2015-04-16
PUBLISHED ONLINE: 2015-10-25
DOI REFERENCE: https://doi.org/10.2298/TSCI1504167Z
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2015, VOLUME 19, ISSUE Issue 4, PAGES [1167 - 1171]
REFERENCES
  1. Metzler, R., Klafter, J. The Random Walks Guide to Anomalous Diffusion: a Fractional Dynamics Approach, Physics Reports, 339 (2000), 1, pp. 1-77
  2. Jiang, X. Y., et al., Exact Solutions of Fractional Schrodinger-Like Equation with a Nonlocal Term, Journal of Mathematical Physics, 52 (2011), ID 042105
  3. He, J.-H. Variational Iteration Method - A Kind of Nonlinear Analytical Technique: Some Examples, International Journal of Non-Linear Mechanics, 34 (1999), 4, pp. 609-708
  4. He, J.-H. Homotopy Perturbation Method: a New Nonlinear Analytical Technique, Applied Mathematics and Computation, 135 (2003), 1, pp. 73-79
  5. Liu, Y. Q. Approximate Solutions of Fractional Nonlinear Equations using Homotopy Perturbation Transformation Method, Abstract and Applied Analysis, 2012 (2012), ID 752869
  6. Khan, Y., et al., An Efficient New Perturbative Laplace Method for Space-Time Fractional Telegraph Equations, Advances in Difference Equations, 2012 (2012), 204
  7. Bulut, H., et al., The Analytical Solution of Some Fractional Ordinary Differential Equations by the Sumudu Transform Method, Abstract and Applied Analysis, 2013 (2013), ID 203875
  8. Jumarie, G. Table of Some Basic Fractional Calculus Formulae Derived from a Modified Riemann- Liouville Derivative for Non-Differentiable Functions, Applied Mathematics Letters, 22 (2009), 3, pp. 378-385
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EFFICIENT HOMOTOPY PERTURBATION METHOD FOR FRACTIONAL NON-LINEAR EQUATIONS USING SUMUDU TRANSFORM

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence