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In this work, we consider a sub-diffusion functional differential equation with an integral condition. We apply the method of semidiscretization in time, to establish the existence and uniqueness of solutions. We also study the continuation of the solution to the maximal interval of existence. By using Rothe’s sequence and values of the fractional integrals over time steps, the results are obtained. Mathematics subject classification (2010): 35R11, 65M20, 34K28.

Existence, uniqueness and continuation of solution of a sub diffusion functional differential equations with an integral condition