We consider Riemann–Liouville fractional differential equations with fractional-order derivative in the impulsive conditions. We study the existence of the mild solution by applying the Laplace transform method and (a,k)-regularized resolvent operator. We use the contraction mapping principle and fixed point theorem for condensing map to prove our existence results.

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In this paper, we prove the existence results for fractional integro-differential equations with fractional order non-instantaneous impulsive conditions. We prove the existence of mild solutions by using the resolvent operator and fixed point theorem for condensing map.

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