Hossein Jafari - Department of Mathematical Sciences, University of South Africa, UNISA۰۰۰۳, South Africa
Sudhanshu Aggarwal - Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur, Uttar Pradesh, India

These days, integral equations govern a wide range of physical processes, including those related to electricity, mechanics, fluid dynamics, ecology, soil moisture dynamics, shallow water wave propagation, and chemical science. As a result, creating new techniques and putting them into practice for solving integral equations becomes more crucial. In this paper, the Upadhyaya integral transform is employed for determining the analytical solutions of the non-linear Volterra integral equations (NVIEs) of the first kind. Four examples suggest the effectiveness of the Upadhyaya integral transform, particularly for NVIEs of the first kind. The calculation results suggest that the proposed method provides accurate solutions to the original problem and this method is a valuable tool for researchers and scientists working on the broader range of problems involving NVIEs of the first kind.

Volterra integral equation, Convolution, Exponential order function, Upadhyaya transform