Convergence and stability of an iteration process and solution of a fractional differential equation
Keyword(s):
AbstractIn this paper, we prove that a three-step iteration process is stable for contractive-like mappings. It is also proved analytically and numerically that the considered process converges faster than some remarkable iterative processes for contractive-like mappings. Furthermore, some convergence results are proved for the mappings satisfying Suzuki’s condition (C) in uniformly convex Banach spaces. A couple of nontrivial numerical examples are presented to support the main results and the visualization is showed by Matlab. Finally, by utilizing our main result the solution of a nonlinear fractional differential equation is approximated.
2011 ◽
Vol 38
(1-2)
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pp. 225-241
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2012 ◽
Vol 52
(1)
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pp. 62-76
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2005 ◽
Vol 167
(1)
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pp. 561-571
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