THERMAL SCIENCE
International Scientific Journal
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
PAPER SUBMITTED: 2014-11-26
PAPER REVISED: 2015-03-10
PAPER ACCEPTED: 2015-04-16
PUBLISHED ONLINE: 2015-10-25
THERMAL SCIENCE YEAR
2015, VOLUME
19, ISSUE
Issue 4, PAGES [1167 - 1171]
- Metzler, R., Klafter, J. The Random Walks Guide to Anomalous Diffusion: a Fractional Dynamics Approach, Physics Reports, 339 (2000), 1, pp. 1-77
- Jiang, X. Y., et al., Exact Solutions of Fractional Schrodinger-Like Equation with a Nonlocal Term, Journal of Mathematical Physics, 52 (2011), ID 042105
- 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
- He, J.-H. Homotopy Perturbation Method: a New Nonlinear Analytical Technique, Applied Mathematics and Computation, 135 (2003), 1, pp. 73-79
- Liu, Y. Q. Approximate Solutions of Fractional Nonlinear Equations using Homotopy Perturbation Transformation Method, Abstract and Applied Analysis, 2012 (2012), ID 752869
- Khan, Y., et al., An Efficient New Perturbative Laplace Method for Space-Time Fractional Telegraph Equations, Advances in Difference Equations, 2012 (2012), 204
- 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
- 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