New existence results on nonlocal neutral fractional differential equation in concepts of Caputo derivative with impulsive conditions

In this article, we examine a nonlinear impulsive neutral fractional differential equation with nonlocal condition in an arbitrary Hilbert space. We obtain an associated integral equation and then consider a sequence of approx-imate integral equations by the projection of considered associated nonlocal neutral fractional integral equation onto finite dimensional space. The existence and uniqueness of an approximate solution by using analytic semi -group theory and the Fixed-point method are demonstrated. Convergence of the solutions of the approximate in-tegral equation is proved. The Faedo-Galerkin approximation of the solution is studied and demonstrated some convergence results. Lastly, the application is presented to illustrate the theory of the main results.(c) 2022 Published by Elsevier Ltd.