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|Paper IPM / M / 8510||
This paper is devoted to investigating the fractional order of con�vergence of operator iteration schemes and, as a means of obtaining rapid convergence, rediscovering fixed-point methods by fractional cal�culus. In addition, a new definition for fractional Gateaux derivative is used which seems a key idea for accelerating the convergence of iterative methods. At the end, the relevance of the theory and applications of integral equations are given.
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