PICARD AND ADOMIAN DECOMPOSITION METHODS FOR A COUPLED SYSTEM OF QUADRATIC INTEGRAL EQUATIONS - El-sayed, A. M. A.; Hashem, H. H. G.; Ziada, E. A. A. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2012)
The comparison between the classical method of successive approximations (Picard) method and Adomian decomposition method was studied in many papers for example ([15] and [37]). In this paper we are concerning with two analytical methods; the classical method of successive approximations (Picard) [18] and Adomian decomposition methods ([1]-[6], [16] and [17]) for a coupled system of quadratic integral equations of fractional order. Also, the existence and uniqueness of the solution and the convergence will be discussed for each method and some examples will be studied.