Application of Laplace Transform Method for Solving Weakly-Singular Integro-Differential Equations

In this paper, the aim is to study the weakly singular integro-differential equations, typically its significance appears in various applications of engineering and science.The contributions of this paper have been presented through the study of existence, uniqueness, and different stability of solution of the weakly singular integro-differential equations, and solving this type of equations analytically.We propose an analytic method based on Laplace transform to solve the weakly singular integro-differential equations, whose advantages lie in simplicity application and obtaining exact solutions.Some suitable examples have been provided to better understand this work and the results of experiments exhibited the proposed method as a simple approach and superiority in accuracy and efficiency of solution.