Abaoub -Shkheam Transform Techniques to Solve Volterra Integral and Volterra Integro-Differential Equations - Nagah A. Elbhilil; Muna I. Bnis; Aml A. Altirban (African Journal of Advanced Pure and Applied Sciences, 2023)
In this research, wide-field integral equations were studied due to their physical, engineering, medical, and other applications. The Abaoub-Shkeam transform was used, which is a mathematical tool that showed results in partial differential and integral equations. It was recently developed to obtain the analytical to the solution for the linear Volterra integral equation of the first type and Also the Volterra equation of the second type and the Volterra differential-integral equation. For this, we assume that the transform kernel is a convolution kernel. Some Applications were shown to demonstrate the efficiency and precision of the Abaoub-Shkheam transform method for resolving types of Volterra integral equations, and Bessel function’s Abaoub-Shkheam transform was inferred.