Sumudu transform of prefunctions and its applications to certain integral, integro differential equations and initial value problems in the bicomplex space
A. Thirumalai, K. Muthunagai, Ritu Agarwal
Received February 5, 2025. Published online November 6, 2025.
Abstract: An integral transform is a useful and simple tool represented by algebraic problems in the process of solving differential equations. Though not as familiar as the other transforms, Sumudu transform has interesting advantages. Because of its scale and unit preserving properties and the ability to solve differential equations without resorting to a new domain, it is considered to be advantageous over the other transforms. Prefunctions possess some of the properties of elementary functions but not periodicity. Extended prefunctions generalise prefunctions. After having obtained the Sumudu and its inverse transform of prefunctions and extended prefunctions, we have analysed them for their properties. The main objective of this article is to obtain closed form solutions for the integral, integro differential equations and initial value problems in terms of prefunctions and extended prefunctions. It is interesting to visualise their solutions using MATLAB for fixed parameters.
Keywords: bicomplex numbers; bicomplex Sumudu transform; prefunction; initial value problem
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Affiliations: A. Thirumalai, K. Muthunagai (corresponding author), Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Chennai-600 127, Tamil Nadu, India, e-mail: thirumalai.a2019@vitstudent.ac.in, muthunagai@vit.ac.in; Ritu Agarwal, Department of Mathematics, Malaviya National Institute of Technology Jaipur, Jaipur-302017, India, e-mail: ragarwal.maths@mnit.ac.in
