A Sumudu Transform Approach to Linear and Nonlinear Volterra Integral Equations
Abstract views: 22
/ 
PDF downloads: 22
Keywords:
Sumudu Transform Method, Integral Equation, Solution, Volterra Equation, Second KindAbstract
This study investigates the effectiveness of the Sumudu transform method in obtaining
analytical solutions for Volterra integral equations of the second kind. Owing to its unique structural
properties particularly its ability to preserve the original function domain and simplify convolution-type
kernels the Sumudu transform provides a powerful alternative to classical integral transform techniques
such as Laplace and Fourier transforms. In this work, we present a systematic framework for applying the
Sumudu transform to Volterra equations with various kernel structures, including separable, convolution,
and weakly singular kernels. The transformed equations are reduced to solvable algebraic forms, enabling
straightforward inversion to obtain closed-form or semi-analytical solutions. Several illustrative examples
are provided to demonstrate the accuracy, simplicity, and computational efficiency of the proposed
approach. The results confirm that the Sumudu transform is an effective and reliable tool for solving a
wide class of Volterra integral equations, offering potential advantages for applications in mathematical
physics, engineering, and applied sciences.
Downloads
References
Watugala, G. K. Sumudu Transform: A New Integral Transform to Solve Differential Equations and Control Engineering International Journal of Mathematical Education in Science and Technology, 24(1), 35–43, 1993.
Belgacem, F. B. M., & Karaballi, A. A. Sumudu Transform Fundamental Properties Investigations and Applications.
Journal of Applied Mathematics and Stochastic Analysis, 2006(1), 1–23, 2006.
Belgacem, F. B. M. Introducing and Analyzing Deeper Sumudu Properties. Nonlinear Studies, 13(1), 23–41, 2006.
Kanwal, R. P. Linear Integral Equations: Theory and Technique. Springer, 2nd Edition, 2013.
Abd Elmohmoud, E. M. Some New Applications of Sumudu Transform for Solution of Linear Volterra Type Integral Equations. International Journal of Science and Research, 11(10), 2022.
Al-Hayani, W. Solving Special Systems of Integral Equations Using the Sumudu Transform with a Semi-Analytical Method. Al-Rafidain Journal of Computer Sciences and Mathematics, 2023.
Almousa, M., Al-Hammouri, A., Almomani, Q., Alomari, M. H., & Alzubaidi, M. M. Sumudu and Elzaki Integral Transforms for Solving Systems of Integral and Ordinary Differential Equations. Advances in Differential Equations and Control Processes, 2024.M. Shell. (2002) IEEEtran homepage on CTAN. [Online]. Available: http://www.ctan.org/tex-
Burton, T. A. Volterra Integral and Differential Equations. Elsevier, 2005.
Debnath, L., & Bhatta, D. Integral Transforms and Their Applications. Chapman & Hall/CRC, 3rd Edition, 2014.
