Fractional Evolution Integro-Differential Systems with Nonlocal Conditions

In this paper, we use the theory of resolvent operators, the fractional powers of operators, fixed point technique and the Gelfand‐Shilov principle to establish the existence and uniqueness of local mild and then local classical solutions of a class of nonlinear fractional evolution integro-differential systems with nonlocal conditions in Banach space. As an application that illustrates the abstract results, a nonlinear nonlocal integro-partial differential system of fractional order is given.

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