Abstract
The primary focus of this paper is to thoroughly examine and analyze a class of a fractional quadraticintegral equation viaζ-generalizedξ-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
Recommended Citation
Ali, Ali Hasan; Abdulqader, Alan Jalal; Redhwan, Saleh S.; Bazighifan, Omar; and Alabdala, Awad T.
(2024)
"Picard and Adomian decomposition methods for a fractionalquadratic integral equation viaζ-generalizedξ-fractional integral,"
Iraqi Journal for Computer Science and Mathematics: Vol. 5:
Iss.
3, Article 42.
DOI: https://doi.org/10.52866/ijcsm.2024.05.03.008
Available at:
https://ijcsm.researchcommons.org/ijcsm/vol5/iss3/42
