International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3957 2020 2020 Department of Science, Applied Science Private University, Jordan Maha Maha Department of Mathematics, Zarqa University, Zarqa , Jordan Gharib M. Gharib Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan; Jadara Research Center, Jadara University, Irbid 21110, Jordan Abdallah Al Al-Husban Department of Mathematics, Zarqa University, Zarqa , Jordan Jeireis A. Abudayyeh Integral equations, including Abel’s integral equation and linear Volterra integral equations of both the first and second kinds and neutrosophic Abel’s integral equation and linear Volterra integral equations of both the first and second kinds, regularly appear in advanced problems across biology, chemistry, physics, and engineering, often modeling systems with memory effects or time-dependent interactions. This study explores the GALM transform as a powerful and unified method for solving these equations. The exact solution of Abel’s integral equation and its neutrosophic version is derived, demonstrating the transform’s simplicity and efficiency through practical applications. Additionally, the GALM transform is employed to solve linear Volterra integral equations of the first and second kinds with their neutrosophic generalizations, with illustrative examples provided to validate its effectiveness. By addressing a wide range of problems, this research establishes the GALM transform as an accurate, reliable, and versatile tool, offering significant advantages over traditional methods in solving complex scientific and engineering equations. 2026 2026 19 35 10.54216/IJNS.270103 https://www.americaspg.com/articleinfo/21/show/3957