New notion of mild solutions for nonlinear differential systems involving Riemann-Liouville derivatives of higher order with non-instantaneous impulses

Abstract

The artefact is dedicated towards the inspection of nonlinear fractional differential systems involving Riemann-Liouville derivative with higher order and fixed lower limit, including non-instantaneous impulses for existence and uniqueness results in Banach spaces. The motive of the paper is to set sufficient conditions to guarantee the existence of mild solution in Banach spaces. Firstly, appropriate integral type initial conditions depending on the impulsive functions are chosen at suitable points. A mild solution of the concerned system is constructed using fractional resolvent. Subsequently, existence and uniqueness results are established under sufficient assumptions utilizing fixed point approach. An example is presented at the end to validate the methodology proposed.