APPLICATIONS OF FRACTIONAL GABOR TRANSFORM
By
V. N. Mahalle1 and S. R. Sawarkar2
1Bar. R. D. I. K. N. K. D. College, Badnera, Maharashtra, India, 444701
2P. R. M. I. T. R., Badnera, Maharashtra, India, 444701
Email: vidyataywade@yahoo.com, sonalisawarkar25@gmail.com
(Received: October 07, 2024; In format: May 06, 2025; Revised: November 14, 2025; Accepted: December 12, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55207
Abstract
Gabor transform is useful tool in applied mathematics to solve number of problems in various fields. Our Fractional Gabor transform adds one more parameter α which removes complexity of problems. Seeing this importance this paper is devoted to some applications of Fractional Gabor transform. We first give Fractional Gabor transform of first order derivative of f(x) and nth order derivative of f(x) with respect to x. Some results which are required for solving Cauchy’s linear differential equation are given here. Solution of Cauchy’s linear differential equation is given. This paper provides some important and basic applications to the solution of some differential equations.
2020 Mathematical Sciences Classification: 46F12.
Keywords and Phrases: Fourier transform, Gabor transform, fractional Gabor transform, testing function space, signal processing.