The Caputo formulation is used to handle fractional derivatives in this study. The well-known method form employs Adomian’s polynomials as the proper mathematical tool for dealing with nonlinear variables. The integral equation may be solved by applying the Sumudu transformation to both sides and then the terms can be written out. The solution is given as a convergent infinite series. Nonlinear Volterra integro-differential equations with fractional derivatives are amenable to the proposed method. The results strongly support the validity, applicability, and efficacy of the approach.