This paper is concerned with the approximation of the solution for neutral fractional differential equation with nonlocal conditions in an arbitrary separable Hilbert space H . We study an associated integral equation and then, consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal neutral fractional integral equation onto finite dimensional space. The sufficient condition for the existence and uniqueness of solutions to every approximate integral equation is derived by using analytic semigroup and Banach fixed point theorem. We demonstrate convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. Moreover, we consider the Faedo-Galerkin approximations of the solution and demonstrate some convergence results. An example is also provided to illustrate the discussed abstract theory.
This work is concerned with a class of neutral functional differential equations with nonlocal history conditions in a Hilbert space. The approximation of solution to a class of such problems is studied. Moreover, the convergence of Faedo–Galerkin approximation of solution is shown. For illustration, an example is worked out.
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.