Application of the Upadhyaya transform to Volterra integral equations of the first kind

Abstract

The application of the methods of integral transforms has tremendously increased during the past many years for finding the exact solutions and the numerical solutions of many new problems arising in the fields of engineering and applied sciences. Some two years back the Upadhyaya transform (https://www.researchgate. net/publication/334033797) was introduced as the most powerful generalization and the most powerful unification of a number of existing variants of the classical Laplace transform occurring in the mathematics research literature. In this paper we apply the Upadhyaya transform for solving the Volterra integral equations of the first kind. Our analysis leads to the conclusion that the Upadhyaya transform is a very powerful tool for finding the solutions to the Volterra integral of the first kind.