Published in Analysis
Discrete analogues of the index transforms, involving Bessel and the modified Bessel functions, are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
Published in International Journal of Applied and Computational Mathematics
In this paper, we introduce the concept of Shehu transform in q-calculus namely q-Shehu transform and establish some properties. We also give some applications of q-Shehu transform for solving some ordinary and partial differential equations with initial and boundary values problems to show its effectiveness and performance of the proposed transfor...
Published in Letters in Mathematical Physics
We discuss a model of a q-harmonic oscillator based on Rogers–Szegő functions. We combine these functions with a class of q-analogs of complex Hermite polynomials to construct a new set of coherent states depending on a nonnegative integer parameter m. Our construction leads to a new q-deformation of the m-true-polyanalytic Bargmann transform whose...
Published in Proceedings - Mathematical Sciences
In this paper, we study the Mexican hat wavelet transform (MHWT) of generalized function space G′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {G}'$$\end{doc...
Published in Journal of Pseudo-Differential Operators and Applications
In this paper, we define and study parameter (p, q)-Boas transform of a signal in linear canonical transform domain. Also, we define the complex signals associated with parameter (p, q)-Boas transform and linear canonical transform and prove the generalized Boas transform product theorem (an analog of Bedrosian’s theorem) in the linear canonical tr...
Published in Complex Analysis and Operator Theory
In the present work we obtain some analogues of the Hilbert formulas on the unit circle for iterated Cauchy-Riemann operator in one-dimensional complex analysis involving higher order Lipschitz classes. Furthermore, a Poincaré-Bertrand formula related to the corresponding singular iterated Cauchy integral over the boundary of a smoothly bounded dom...
Published in Banach Journal of Mathematical Analysis
For μ,β∈R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu , \beta \in {\mathbb {R}}$$\end{document}, we introduce and study in detail the generalized Stieltjes opera...
Published in International Journal of Applied and Computational Mathematics
We introduce the short-time fractional Fourier transform with a suitable quaternion valued function as the window function on the space of square integrable quaternion valued functions on R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \use...
Published in Partial Differential Equations and Applications
A multi-domain spectral method is presented to compute the Hilbert transform on the whole compactified real line, with a special focus on piece-wise analytic functions and functions with algebraic decay towards infinity. Several examples of these and other types of functions are discussed. As an application solitons to generalized Benjamin–Ono equa...
Published in International Journal of Applied and Computational Mathematics
In this article, we adopt the modified decomposition method (MDM) to find definite results of three different types of first order nonlinear ordinary differential equations that involves algebraic and transcendental functions and one second order ODE together with initial conditions. The MDM involves techniques of the natural transform method and a...
