ON THE EXISTENCE OF SOLUTIONS IN COUPLED SYSTEM OF NON-LINEAR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS ON THE HALF LINE

In the present work we discuss the existence of solutions for a system of nonlinear fractional integro-differential equations with initial conditions. This system involving the Caputo fractional derivative and Riemann¡Liouville fractional integral. Our results are based on a fixed point theorem of Schauder combined with the diagonalization method.