Volume 27 , Issue 1 , PP: 19-35, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Maha Alsaoudi 1 * , Gharib M. Gharib 2 , Abdallah Al-Husban 3 , Jeireis A. Abudayyeh 4
Doi: https://doi.org/10.54216/IJNS.270103
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.
Linear Volterra integral equations of the first and second kinds , Abel&rsquo , s integral equation , Neutrosophic Abel's equation , Neutrosophic integral equation , GALM transform , Convolution theorem , Inverse GALM transform
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