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This paper is divided in two parts. In the first part, we prove coercivity results and minimization of the Euler energy functional. In the second part, we focus on the existence and multiplicity of a positive solution of fractional Dirichlet problem involving the $\gamma(\xi)$-Laplacian equation with non-negative weight functions in $\mathcal{H}^{\alpha,\beta;\chi}_{\gamma(\xi)}(\Lambda,\mathbb{R})$ using some variational techniques and Nehari manifold., Comment: 14 pages

In this paper, we extend the coupled fractional Fourier transform of a complex valued functions to that of the quaternion valued functions on $\mathbb{R}^4$ and call it the quaternion coupled fractional Fourier transform (QCFrFT). We obtain the sharp Hausdorff-Young inequality for QCFrFT and obtain the associated R\`enyi uncertainty principle. We also define the short time quaternion coupled fractional Fourier transform (STQCFrFT) and explore its important properties followed by the Lieb's and entropy uncertainty principles.

Making use of the Hankel determinant and the Ruscheweyh derivative, in this work, we consider a general subclass of m-fold symmetric normalized bi-univalent functions defined in the open unit disk. Moreover, we investigate the bounds for the second Hankel determinant of this class and some consequences of the results are presented. In addition, to demonstrate the accuracy on some functions and conditions, most general programs are written in Python V.3.8.8 (2021)., Comment: 16 pages, 7 figures

In this paper, using a new shrinking projection method and generalized resolvents of maximal monotone operators and generalized projections, we consider the strong convergence for finding a common point of the fixed points of a Bregman quasi-nonexpansive mapping, and common fixed points of a infinite family of Bregman weak relatively nonexpansive mappings, and common zero points of a finite family of maximal monotone mappings, and common solutions of an equilibrium problem in a reflexive Banach space., Comment: 28 pages. arXiv admin note: substantial text overlap with arXiv:2107.13254

In this paper, using the Bregman distance, we introduce a new projection-type algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points. Then the strong convergence of the sequence generated by the algorithm will be established under suitable conditions. Finally, using MATLAB software, we present a numerical example to illustrate the convergence performance of our algorithm., Comment: 19 pages

A Strong Convergence Theorem for finite families of Bregman Demimetric Mappings in a Banach Space under a New Shrinking projection Method, Comment: 24 pages

With the increasing importance of the Mittag-Leffler function in the physical applications, these days many researchers are studying various generalizations and extensions of the Mittag-Leffler function. In this paper efforts are made to define bicomplex extension of the Mittag-Leffler function and also its analyticity and region of convergence are discussed. Various properties of the bicomplex Mittag-Leffler function including integral representation, recurrence relations, duplication formula and differential relations are established.

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends(Thong et al, Numerical Algorithms. 78, 1045-1060 (2018)). We have reduced and refined some of their algorithm's conditions and we have proved the convergence of the algorithm in the presence of some computational errors. Then using MATLAB software, the result will by illustrated in some numerical examples. Finally, we compare our algorithm with some other well known algorithms., Comment: 13 pages

In this paper, we study regularity of weak solutions to the incompressible Boussinesq equations in $\mathbb{R}^{3}\times (0,T)$. The main goal is to establish the regularity criterion in terms of one velocity component and the gradient of temperature in Lorentz spaces., Comment: arXiv admin note: text overlap with arXiv:2005.03377