In this paper, we introduce and investigate the Directional Short-Time Free Metaplectic Transform (DSTFMT), a novel time–frequency representation associated with free symplectic matrices. This framework unifies the directional short-time Fourier transform with the free metaplectic theory, encompassing several classical operators such as directional fractional Fourier transform, Fresnel, and linear canonical transforms as special cases. We establish fundamental structural properties of the DSTFMT, including its representation as a metaplectic transform of a directionally windowed function, orthogonality relations, an exact inversion formula, and a Plancherel-type identity. Furthermore, we prove a Hausdorff–Young inequality, derive a Pitt-type weighted inequality, and establish a logarithmic uncertainty principle in the metaplectic setting. These results extend several classical inequalities in harmonic analysis to a directional and symplectic time–frequency framework. The proposed transform provides a unified approach to directional phase-space analysis and offers potential applications in signal processing, quantum mechanics, and optical systems governed by symplectic structures.

In this paper, we investigate geometric function theoretic properties of a normalized fractional integral operator constructed from the Riemann–Liouville fractional integral combined with the generalized Marcum Q-function. In the first part, we establish sufficient conditions under which the operator is starlike or convex of order α in the unit disk. In the second part, we study convolution properties of the operator, providing conditions under which it maps functions in the class ℛ(β ) into ℛ(σ ) and belongs to the Hardy space ℋ^∞(𝔻) . The analysis relies on techniques from differential subordination, admissible functions, and classical tools from geometric function theory, highlighting the rich interplay between fractional calculus and the generalized Marcum Q-function.

In this study, we focus on the Jensen-Mercer inequality and the Montgomery-Mercer identity to develop new error bounds for Ostrowski quadrature schemes. To wrap up this task, initially, we introduce a new equality connected to Montgomery's identity invoking the Mercer concept. We then apply the Montgomery-Mercer identity to establish some updated bounds for rectangular and mid-point schemes involving convex mappings and famously known inequalities like Holder's and power-mean. Also, we explore some special cases that stem from our main findings, conduct numerical tests, visual analysis, and present applications related to means.

In this paper, we establish new Tur & aacute;n type inequalities for sections of some class of functions related to the generalized hypergeometric functions (Fox-Wright functions). The main mathematical tools of some of the main results are based on some new integral representations for the sections of hypergeometric functions and some monotonicity criterion of quotient of gamma function. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Developing two-step fractional numerical methods for finding the solution of nonlinear equations is the main objective of this research article. In addition, we present a detailed study of convergence analysis for the methods that have been proposed. By comparing numerically, we can see that the proposed methods significantly improve convergence rate and accuracy. Additionally, we demonstrate how our main results can be applied to basins of attraction.

This study uses Raina’s function to obtain a new coordinated pq-integral identity. Using this identity, we construct several new pq-Simpson’s type inequalities for generalized convex functions on coordinates. Setting p1=p2=1 in these inequalities yields well-known quantum Simpson’s type inequalities for coordinated generalized convex functions. Our results have important implications for the creation of post quantum mathematical frameworks.

In the present paper, we prove the monotonicity property of the ratios of the generalized Volterra function. As consequences, new and interesting monotonicity concerning ratios of the exponential integral function, as well as it yields some new functional inequalities including Turán-type inequalities. Moreover, two-side bounding inequalities are then obtained for the generalized Volterra function. The main mathematical tools are some integral inequalities. As applications, a few of upper and lower bound inequalities for the exponential integral function are derived. The various results, which are established in this paper, are presumably new, and their importance is illustrated by several interesting consequences and examples accompanied by graphical representations to substantiate the accuracy of the obtained results. Some potential directions for analogous further research on the subject of the present investigation are indicated in the concluding section.

Integral inequalities are the proficient aspect of mathematical analysis. Various techniques have been deployed to acquire to fresh inequalities which are beneficial in various area problems. The aim of this paper is to derive some new analytic inequalities involving generalized weighted exponential beta functions. To attain our primary objectives, we introduce the generalized exponential function X-rho,X-b,X-delta(pi) and weighted form of exponential beta functions F(rho,b,delta). Furthermore, we briefly discuss their properties. we derive several inequalities in association with X-rho,X-b,X-delta (pi) and F(rho,b,delta). As the applications of these new developments,we conclude some error estimates of Ostrwoski's type inequalities, which show the significance of the obtained results.

In statistical process control, the control charts are an effective tool to monitor the process. When the process is examined based on an exponential family distributed response variable along with a single explanatory variable, the generalized linear model (GLM) provides better estimates and GLM-based charts are preferred. This study is designed to propose GLM-based control charts using different link functions (i.e., logit, probit, c-log-log, and cauchit) with the binary response variable. The Pearson residuals (PR)- and deviance residuals (DR)-based control charts for logistic regression are proposed under different link functions. For evaluation purposes, a simulation study is designed to evaluate the performance of the proposed control charts. The results are compared based on the average run length (ARL). Moreover, the proposed charts are implemented on a real application for COVID-19 death monitoring. The Monte Carlo simulation study and real applications show that the performance of the model-based control charts with the c-log-log link function gives a better performance as compared to model-based control charts with other link functions.

By using the q-Jackson integral and some elements of the q-harmonic analysis associated with the q-Hankel transform, we introduce and study a q-analog of the Hankel–Stockwell transform. We present some properties from harmonic analysis (Plancherel formula, inversion formula, reproducing kernel, etc.). Furthermore, we establish a version of Heisenberg’s uncertainty principles. Finally, we study the q-Hankel–Stockwell transform on a subset of finite measure.

In this paper, using the [Formula: see text]-Jackson integral and some elements of the [Formula: see text]-harmonic analysis associated with the [Formula: see text]-Hankel transform, we introduce and study the [Formula: see text]-analogue of the Hankel–Stockwell transform. We give some harmonic analysis properties (Plancherel formula, inversion formula, reproduicing kernel[Formula: see text]). Furthermore, we establish a version of Heisenberg’s uncertainty principles. Last, we study the [Formula: see text]-Hankel–Stockwell transform on subset of finite measure.

In this paper, we generalize the continuous quaternion shearlet transform on $${\mathbb {R}}^{2}$$ to $${\mathbb {R}}^{2d}$$ , called the multivariate two sided continuous quaternion shearlet transform. Using the two sided quaternion Fourier transform, we derive several important properties such as (reconstruction formula, plancherel’s formula, etc.). We present several example of the multivariate two sided continuous quaternion shearlet transform. We apply the multivariate two sided continuous quaternion shearlet transform properties and the two sided quaternion Fourier transform to establish the Heisenberg uncertainty principle. Last we study the multivariate two sided continuous quaternion shearlet transform on subset of finite measures.

The fractional Fourier transform (FrFT) is one of the generalizations of the Fourier transform (FT). This paper is centered on the compression of different forms of signal in FrFT domain in order to extract some properties of each one with a comparison between the FrFT and the usual FT. Also, our focus here will be on two qualitative uncertainty principles for the fractional Fourier transform: The Cowling–Price’s theorem and the L^p-L^q version of Morgan’s theorem for the FrFT. These two results estimate the decay of two fractional Fourier transforms F_α(f) and F_γ (f) , with γ -α nπ , ∀ n∈ℤ , which allows us to deduce the usual uncertainty principles between a function f and its fractional Fourier transform F_γ(f) .

In this paper, we state some new versions of the famous Ramanujan Master Theorem via the q-two dimensional Mellin transform. As applications, some values of Jackson's q-double integrals involving q-special functions are computed.

The fractional Fourier transform (FrFT) is a generalization of the usual Fourier transform. The aim of this paper is to show the compression of sound signal in FrFT domain and to prove the qualitative and quantitative uncertainty principles for the FrFT. The first of these results consists the Hardy’s and an $$L^p-L^q$$ version of Miyachi’s theorems for the FrFT, which estimates of decay of two fractional Fourier transforms $$F_{\alpha }(f)$$ and $$F_{\gamma } (f)$$ , with $$\gamma -\alpha \ne n\pi , \forall n\in \mathbb {Z}$$ . The second result consists an extension of Faris’s local uncertainty principle which states that if a non zero function $$F_{\alpha }(f) \in L^2(\mathbb {R})$$ is highly localized near a single point then $$F_{\gamma } (f)$$ cannot be concentrated in a set of finite measure with $$\gamma -\alpha \ne n\pi , \forall n\in \mathbb {Z}$$ . From our results we deduce the usual uncertainty principles for the fractional Fourier transform which states these theorems between a function f and its fractional Fourier transform $$F_{\gamma }(f)$$ .

In this paper, we study the quaternion windowed Fourier transform and prove the Beckner's uncertainty principle in term of entropy, Lieb uncertainty principle and the Heisenberg uncertainty principle for the quaternion windowed Fourier transform, the radar quaternion ambiguity function and the quaternion-Wigner transform.

In this paper, we present some new elements of harmonic analysis related to the right-sided multivariate continuous quaternion wavelet transform. The main objective of this article is to introduce the concept of the right-sided multivariate continuous quaternion wavelet transform and investigate its different properties using the machinery of multivariate quaternion Fourier transform. Last, we have proven a number of uncertainty principles for the right-sided multivariate continuous quaternion wavelet transform.

In this paper, we present some new elements of harmonic analysis related to multivariate continuous shearlet transform introduced earlier in Dahlke et al. (J Fourier Anal Appl 16:340–364, 2010; The continuous shearlet transform in arbitrary space dimensions, Philipps-Universität Marburg, Marburg, 2008). Thus, some results (Parseval’s formula, inversion formula, etc.) are established. Next, we prove an analogue of Heisenberg’s inequality for shearlet transform. Last, we study shearlet transform on subset of finite measures.

In this paper, we present some new elements of harmonic analysis related to the continuous quaternion shearlet transform .The main objective of this article is to introduce the concept of the quaternionic Shearlet transform and investigate its different properties using the machinery of quaternion Fourier transforms and quaternion convolution. Moreover, we derive the classical Heisenberg–Pauli–Weyl inequality. Last, we study quaternion shearlet transform on subset of finite measure.

In this paper we propose a novel transform called continuous quaternionic stockwell transform. We express the admissibility condition in term of the (two-sided) quaternion Fourier transform . We show that its fundamental properties, such as Plancherel, Parseval and inversion formula, can be established whenever the continuous quaternion stockwell satisfy a particular admissibility condition. We present several examples of the continuous quaternion stockwell transform. We apply the continuous quaternion stockwell transform properties and the two sided quaternion Fourier transform to establish a number of uncertainty principle for these extended Stockwell .