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The fractional Fourier–Jacobi wavelet transform
The main aim of this work is to define the fractional Jacobi translation, the fractional Jacobi convolution and to study the fractional...
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A sparse approximation for fractional Fourier transform
The paper promotes a new sparse approximation for fractional Fourier transform, which is based on adaptive Fourier decomposition in Hardy-Hilbert...
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Fractional Fourier transform for space–time algebra-valued functions
The aim of this article is to introduce a fractional space–time Fourier transform (FrSFT) by generalizing the fractional Fourier transform for...
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Uncertainty principles of hypercomplex functions for fractional Fourier transform
In the present paper, different uncertainty principles for hypercomplex functions associated with the fractional Fourier transform (FRFT) are...
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Fourier Transform
Fourier transforms of integrable functions defined on the whole real line...
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On the fractional Opdam–Cherednik transform
In the present paper, we study a new harmonic analysis in the setting of the Opdam–Cherednik. We establish the fractional Opdam–Cherednik transform...
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Fourier Transform of the Summatory Abel–Poisson Function
The authors consider the current issues of the optimal decision theory, namely, the analysis of the asymptotic properties of the Fourier transform of...
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Quaternion Fourier Transform
This chapter first focusses on the theoretical foundations of quaternion Fourier transforms. Basically, in the complex Fourier transform the...
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Efficient Finite Difference/Spectral Method for the Time Fractional Ito Equation Using Fast Fourier Transform Technic
A finite difference/spectral scheme is proposed for the time fractional Ito equation. The mass conservation and stability of the numerical solution...
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Fractional Bessel Derivative Within the Mellin Transform Framework
In this paper, we present a fresh perspective on the fractional power of the Bessel operator using the Mellin transform. Drawing inspiration from the...
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Fractional Jacobi-Dunkl transform: properties and application
The aim of this paper is to develop a novel harmonic analysis in the Jacobi-Dunkl setting. We propose the fractional Jacobi-Dunkl transform in order...
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Short time coupled fractional fourier transform and the uncertainty principle
In this paper, we introduce a short-time coupled fractional Fourier transform ( scfrft ) using the kernel of the coupled fractional Fourier transform ( cfrft...
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Mittag–Leffler–Hyers–Ulam Stability of Delay Fractional Differential Equation via Fractional Fourier Transform
This paper deals with existence and Mittag–Leffler–Hyers–Ulam stability of solution for a fractional order differential equation involving...
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Quaternionic short-time fractional Fourier transform
We introduce the short-time fractional Fourier transform with a suitable quaternion valued function as the window function on the space of square...
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Fractional Fourier transform on ℝ2 and an application
We focus on the L p (ℝ 2 ) theory of the fractional Fourier transform (FRFT) for 1 ⩽ p ⩽ 2. In L 1 (ℝ 2 ), we mainly study the properties of the FRFT via...