A Study on ‎‎Functional Fractional Integro-Differential Equations ‎of Hammerstein type

In this paper, functional Hammerstein integro-differential equations of fractional order is studied. Here the existence and uniqueness of the solution is proved. A numerical method to approximate the solution of problem is also presented which is based on an improvement of the successive approximations method. Error estimation of the method is analyzed and error bound is obtained. The convergence and stability of the method are proved. At the end, application of the method is revealed by presenting some examples.

Keywords:

Functional Hammerstein integro-differential equations , Fractional order , Successive approximations‎‎ , ‎Spline interpolation‎ , Trapezoidal quadrature rule