Published on: August 2026
A PARAMETERIZED ADAPTIVE KERNEL INTEGRAL TRANSFORM WITH GAUSSIAN DAMPING: MATHEMATICAL PROPERTIES AND CONVERGENCE ANALYSIS
Deore Manoj Uttam
Article Status
Available Documents
Abstract
In this paper, a parameterized integral transform, referred to as the Adaptive Kernel Integral Transform (AKIT), is introduced through the kernel
The parameter α introduces an additional Gaussian-type damping mechanism, whereas β provides a linear weighting factor. The proposed kernel is investigated with respect to continuity, positivity, smoothness, decay, and parameter dependence. Sufficient conditions for the existence and convergence of the proposed transform are established. It is also shown that the classical Laplace transform is recovered when α = β =0. Selected standard functions are considered, and a class of rapidly growing functions of the form is investigated. In particular, for and , the classical Laplace transform diverges, whereas the proposed transform converges for every , under the stated conditions. A comparison with the classical Laplace transform is presented together with a numerical and graphical illustration. The results indicate that the proposed kernel provides a flexible parameterized framework for studying selected classes of functions for which an additional quadratic damping mechanism is analytically useful.
Keywords: Adaptive Kernel Integral Transform, Parameterized Kernel, Gaussian Damping, Laplace Transform, Integral Transform, Convergence, Kernel Function.
How to Cite this Paper
Uttam, D. M. (2026). A Parameterized Adaptive Kernel Integral Transform with Gaussian Damping: Mathematical Properties and Convergence Analysis. International Journal of Creative and Open Research in Engineering and Management, <i>02</i>(8), 1-14. https://doi.org/10.55041/ijcope.v2i8.248
Uttam, Deore. "A Parameterized Adaptive Kernel Integral Transform with Gaussian Damping: Mathematical Properties and Convergence Analysis." International Journal of Creative and Open Research in Engineering and Management, vol. 02, no. 8, 2026, pp. 1-14. doi:https://doi.org/10.55041/ijcope.v2i8.248.
Uttam, Deore. "A Parameterized Adaptive Kernel Integral Transform with Gaussian Damping: Mathematical Properties and Convergence Analysis." International Journal of Creative and Open Research in Engineering and Management 02, no. 8 (2026): 1-14. https://doi.org/https://doi.org/10.55041/ijcope.v2i8.248.
Search & Index
References
- Debnath & Bhatta — Integral Transform TheoryL. Debnath and D. Bhatta, Integral Transforms and Their Applications, 3rd ed., CRC Press, Boca Raton, 2014.
- Widder — Classical Laplace Transform D. V. Widder, The Laplace Transform, Princeton University Press, Princeton, 1941; later Princeton editions.
- Sneddon — Integral Transform ApplicationsI. N. Sneddon, The Use of Integral Transforms, McGraw-Hill, New York, 1972.
- Erdélyi et al. — Tables of Integral TransformsA. Erdélyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Tables of Integral Transforms, Vol. I, McGraw-Hill, New York, 1954.
- Schiff — Laplace TransformJ. L. Schiff, The Laplace Transform: Theory and Applications, Springer, 1999.
- Kim — Laplace-type integral transformsH. Kim, "The Intrinsic Structure and Properties of Laplace-Typed Integral Transforms," Mathematical Problems in Engineering, 2017, Article ID 1762729.
- Jafari — General Integral TransformH. Jafari, "A New General Integral Transform for Solving Integral Equations," Journal of Advanced Research, vol. 32, pp. 133–138, 2021.
- Fahad, Rehman & Fernandez — Generalized Laplace Framework H. M. Fahad, M. U. Rehman, and A. Fernandez, "On Laplace Transforms With Respect to Functions and Their Applications to Fractional Differential Equations," Mathematical Methods in the Applied Sciences, vol. 46, no. 7, pp. 8304–8323, 2023.
- Ata & Kıymaz — Generalized Laplace TransformE. Ata and I. O. Kıymaz, "A New Generalized Laplace Transform and Its Applications to Fractional Bagley-Torvik and Fractional Harmonic Vibration Problems," Miskolc Mathematical Notes, vol. 24, no. 2, pp. 597–610, 2023.
- Murugan, Ganesa Moorthy & RamasamyA. Murugan, C. Ganesa Moorthy, and C. T. Ramasamy, "A New Generalized Laplace Transform," International Journal of Nonlinear Analysis and Applications, vol. 16, no. 9, pp. 1–6, 2025
Ethical Compliance & Review Process
- •All submissions are screened under plagiarism detection.
- •Review follows editorial policy.
- •Authors retain copyright.
- •Peer Review Type: Double-Blind Peer Review
- •Published on: Aug 28 2026
This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. You are free to share and adapt this work for non-commercial purposes with proper attribution.