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Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
eISSN: 2320-3226
pISSN: 0970-6577
Impact Factor: 4.895 (2017)
DOI: 10.5958/2320-3226
Editor-in-Chief:  Prof. Dr. Lalit Mohan Upadhyaya
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Article Details

Bulletin of Pure and Applied Sciences- Math& Stat. (Started in 1982)
Year : 2021, Volume & Issue : BPAS-Maths & Stat 40E(2), JUL-DEC 2021
Page No. : 140-148, Article Type : Original Aticle
Article DOI : 10.5958/2320-3226.2021.00016.3 Communicated, edited and typeset in Latex by Jyotindra C. Prajapati (Editor). Received April 21, 2020 / Revised August 26, 2021 / Accepted September 21, 2021. Online First Published on December 17, 2021)

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

Adil Mousa 1
Author’s Affiliation : 1. Department of Mathematics, Faculty of Science and Technology, Omdurman Islamic University, Khartoum, Sudan. 1. E-mail: [email protected]

Corresponding Author : Adil Mousa,
E-Mail:-[email protected]


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.

2020 Mathematics Subject Classification:  34A12, 44A05, 44A99, 45D05, 45D99.


Upadhyaya transform, Inverse Upadhyaya transform, Volterra integral equations, Convolution theorem, Bessel function.
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