The article is dedicated towards the study of fractional-order non-linear differential systems with non-instantaneous impulses involving Riemann-Liouville derivatives with fixed lower limit and appropriate integral type initial conditions in Banach spaces. First, mild solution of the system is constructed and subsequently, its existence is proven using Banach’s fixed point theorem. Then, results of approximate controllability are established using the concept of fractional semigroup and an iterative technique. Suitable examples are given in the end supporting the methodology along with pointing out corrections in examples presented in previous articles.

The article is dedicated towards the study of fractional order non-linear differential systems with non-instantaneous impulses involving Riemann-Liouville derivatives with fixed lower limit and appropriate integral type initial conditions in Banach spaces. First, mild solution of the system is constructed and subsequently its existence is proven using Banach's fixed point theorem. Then, results of approximate controllability are established using concept of fractional semigroup and an iterative technique. Suitable examples are given in the end supporting the methodology along with pointing out correction in examples presented in previous articles.

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

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