Abstract
This research outlines a reliable strategy for finding a solutions of nonlinear quadratic integro-differential equation of fractional order (FQIDEs). Local and global existence theorems of solutions of the FQIDEs have been obtained by using Schauder’s and Tychonoff fixed point theorems. The fractional derivative is described in the Caputo sense. The Laplace decomposition method (LDM) and modified Adomian decomposition method (MADM) are described to be fast and accurate. Illustrative examples are included to demonstrate the efficiency and reliability of presented techniques.