D.‎‎ Nazari ‎Susahab‎ - Department of Mathematics‎, ‎Azarbaijan Shahid Madani University‎, ‎Tabriz‎, ‎Iran‎.
M. Jahanshahi - Department of Mathematics‎, ‎Azarbaijan Shahid Madani University‎, ‎Tabriz‎, ‎Iran‎.

The aim of this paper is solving nonlinear Volterra-Fredholm fractional integro-differential equations with mixed boundary conditions‎. ‎The basic idea is to convert fractional integro-differential equation to a type of second kind Fredholm integral equation‎. ‎Then the obtained Fredholm integral equation will be solved with Nystr\"{o}m and Newton-Kantorovitch method‎.  ‎Numerical tests for demonstrating the accuracy of the method is ‎included.‎

Fractional integro-differential equations, Boundary mixed Conditions, Nystr\"{o}m method, Newton-Kantorovitch ‎method.‎