Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 14, Issue 5, Pages 1978-1983Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2008.07.006
Keywords
Analytical approximations; Homotopy analysis method; Nonlinear fractional differential equation; Caputo fractional derivative
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Funding
- National Natural Science Foundation of China [50739004]
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In this paper, we apply the homotopy analysis method (HAM) to solve the fractional Volterra's model for Population growth of a species in a closed system. This technique is extended to give solutions for nonlinear fractional integro-differential equations. The whole HAM solution procedure for nonlinear fractional differential equations is established. Further, the accurate analytical approximations are obtained for the first time, which are valid and convergent for all time t. This indicates the validity and great potential of the homotopy analysis method for solving nonlinear fractional integro-differential equations. (C) 2008 Elsevier B.V. All rights reserved.
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