In this paper, we investigate existence and approximation of solutions of fractional order iterative differential equations by virtue of nonexpansive mappings, fractional calculus and fixed point methods. Three existence theorems as well as convergence theorems for a fixed point iterative method designed to approximate these solutions are obtained in two different work spaces via Chebyshev’s norm, Bielecki’s norm and β norm. Finally, an example is given to illustrate the obtained results.
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