Abstract
This manuscript aims to investigate the existence and approximate controllability results for integral solution of nondensely defined Hilfer neutral differential inclusion system of Sobolev-type with infinite delay and non-instantaneous impulse in a Hilbert space. By utilizing the semigroup theory of bounded linear operators, fixed point technique, fractional calculus, and the theory of multivalued maps, the principal discussions are demonstrated. The sufficient conditions for the existence and approximate controllability are demonstrated under the consideration that the linear operator A is defined nondensely and satisfies the Hille–Yosida condition. Finally, an example is given to support the validity of the study.
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