Picard and Adomian decomposition methods for a fractional quadratic integral equation via generalized fractional integral

Abstract

 The primary focus of this paper is to thoroughly examine and analyze a class of a fractional quadraticintegral equation via generalized fractional integral. To achieve this, we introduce an operator that possessesfixed points corresponding to the solutions of the fractional quadratic integral equation, effectively transforming thegiven equation into an equivalent fixed-point problem. By applying the Banach fixed-point theorems, we prove theuniqueness of solutions to fractional quadratic integral equation. Additionally, The Adomian decomposition methodis used, to solve the resulting fractional quadratic integral equation. This technique rapidly provides convergentsuccessive approximations of the exact solution to the given fractional quadratic integral equation, therefore, weinvestigate the convergence of approximate solutions, using the Adomian decomposition method. Finally, we providesome examples, to demonstrate our results. Our findings contribute to the current understanding of fractionalquadratic integral equation and their solutions and have the potential to inform future research in this area.