Faedo-Galerkin approximation of solution for a nonlocal neutral fractional differential equation with deviating argument
In this paper, the authors study the existence of solutions of a class of nonlocal neutral fractional differential equations with deviating argument in a separable Hilbert space. They obtain an associated integral equation and then, consider a sequence of approximate integral equations. They investigate the existence and uniqueness of the mild solution for every approximate integral equation by using analytic semigroup theory and the Banach fixed point theorem. Next, the authors demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. The Faedo-Galerkin approximation of the solution is studied and some convergence results are established. An example is provided to illustrate the theory.
neutral fractional differential equation with deviating argument
scientific article; zbMATH DE number 6661821
scientific article