Existence of a mild solution for a fractional impulsive differential equation of the Sobolev type including deviating argument

The impulsive fractional differential equation of the Sobolev type, including deviating arguments, is the subject of the study. The analytic semigroup and fixed point approaches serve the purpose of determining the existence of the approximations. The fractional power of a closed linear operator concept is used to show how the approximation converges. To arrive at a unique approach, an approximation strategy is used. Our main conclusions are defined using an example.