EXISTENCE AND APPROXIMATIONS OF SOLUTIONS TO SOME FRACTIONAL ORDER FUNCTIONAL INTEGRAL EQUATIONS

摘要

In this paper we shall study a fractional order functional integral equation. In the first part of the paper,we proved the existence and uniqueness of mild and global solutions in a Banach space. In the second part of the paper, we used the analytic semigroups theory of linear operators and the fixed point method to establish the existence, uniqueness and convergence of approximate solutions of the given problem in a separable Hilbert space. We also proved the existence and convergence of Faedo-Galerkin approximate solution to the given problem. Finally, we give an example.