Existence and stability results for a nonlinear implicit fractional differential equation with a discrete delay

In this paper, we are concerned with a class of nonlinear implicit fractional di?erential equation with adiscrete delay. By means of the contraction mapping principle, we prove the existence of a unique solution.Then, we investigate the continuous dependence of the solution upon the initial delay data and the Ulamstability.

Keywords:

Fractional differential equation, discrete delay, existence and continuous dependence of solution on initial data, Ulam stability Banach fixed point theorem,

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