An analytical solution with existence and uniqueness conditions for fractional integro-differential equations

This study aims to apply the two-step Adomian decomposition method (TSADM) to find an analytical solution of integro-differential equations for fractional order without discretization/approximation with less number of iterations and reduce the computational efforts. Moreover, we have established the results for the existence and uniqueness of a solution with the help of some fixed point theorems and the Banach contraction principle. Furthermore, the method is demonstrated on different test examples arising in real life situations. It is concluded that the TSADM provides exact solution of the fractional integro-differential equations in one iteration. At the same time, the other existing methods furnish an approximate solution and require lots of computation to solve the problem applying discretization/approximation on fractional operators.