Some new results on nonlinear fractional iterative Volterra-Fredholm integro differential equations

Abstract

In this paper, we establish some new results concerning the existence and uniqueness of the solutions of iterative nonlinear Volterra-Fredholm integro differential equations subject to the initial conditions. The fractional derivatives are considered in the Caputo sense. Also these new results are obtained by applying the GronwallBellman’s inequality and the Banach contraction fixed point theorem. Moreover, the results of references [16, 17, 27] appear as a special case of our results.