Mathematics and Computational Sciences

Upadhyaya integral transform: A tool for solving non-linear Volterra integral equations

Document Type : Original Article

Authors

Hossein Jafari 1
Sudhanshu Aggarwal 2

1 Department of Mathematical Sciences, University of South Africa, UNISA0003, South Africa

2 Department of Mathematics, National Post Graduate College, Barhalganj, Gorakhpur, Uttar Pradesh, India

https://doi.org/10.30511/mcs.2024.2029301.1174
Abstract
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.

Keywords

Volterra integral equation
Convolution
Exponential order function
Upadhyaya transform

Subjects

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Mathematics and Computational Sciences
Volume 5, Issue 2
Spring 2024
Pages 63-71

  • Receive Date 15 May 2024
  • Revise Date 08 June 2024
  • Accept Date 21 June 2024

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