Existence criteria and solution search by the analytic technique of functional integral equation

Existence of a solution of the functional integral equation in an unbounded interval involving the Riemann–Liouville operator is investigated. Here sufficient conditions in the context of existence and stability are derived by employing hybridized fixed point theory in the Banach algebra setting. Further, an example is presented to showcase the validity of the obtained result. Moreover, the solution of the example in closed form is estimated by the semianalytic technique which is being driven by a modified homotopy perturbation method in conjunction with the Adomian decomposition method.