This paper gives sufficient conditions for the existence of positive periodic solutions to general indefinite singular differential equations. Furthermore, under some assumptions we show the existence of two positive periodic solutions. The methods used are Krasnoselski\(\breve{\mbox{i}}\)’s-Guo fixed point theorem and the positivity of the associated Green’s function.

Fusion frames and subfusion frames are generalizations of frames in the Hilbert spaces. In this paper, we study subfusion frames and the relations between the fusion frames and subfusion frame operators. Also, we introduce new construction of subfusion frames. In particular, we study atomic resolution of the identity on the Hilbert spaces and derive new results.

In this work, a new class of bi-univalent functions \(I^{n+1}_{\Gamma_m,\lambda}(x,z)\) is defined by means of subordination. Upper bounds for some initial coefficients and the Fekete-Szegö functional of functions in the new class were obtained.

This work is a generalization of Ostrowski type integral inequalities using a special 4-step quadratic kernel. Some new and useful results are obtained. Applications to Quadrature Rules and special Probability distribution are also evaluated.

In this work, we establish the existence and uniqueness of solution of Floquet eigenvalue and its adjoint to homogeneous growth-fragmentation equation with positive and periodic coefficients. We study the Floquet exponent, which measures the growth rate of a population. Finally, we establish the long term behavior of solution to the homogeneous growth-fragmentation equation by entropy method [1,2,3].

In mathematical chemistry, a large number of topological indices are used to predict the physicochemical properties of compounds, especially in the study of quantitative structure-proerty relationship (QSPR).
However, many topological indices have almost the same predictive ability. In this paper, we focus on how to use fewer topological indices to predict the physicochemical properties of compounds through the QSPR analysis of connectivity indices of benzene hydrocarbons.

The main goal of this brief article is to provide an elementary proof of Sun’s six conjectures on Apéry-like sums involving ordinary harmonic numbers.

In this paper, we develop a new application of the Laplace transform method (LTM) using the series expansion of the dependent variable for solving fractional logistic growth models in a population as well as fractional prey-predator models. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method some examples are provided. The results reveal that the technique introduced here is very effective and convenient for solving fractional-order nonlinear differential equations.

The generation of coefficients of terms of positive and negative powers of \(n\) and \(-n\) of Kifilideen trinomial theorem as the terms are progress is stressful and time-consuming which the same problem is identified with coefficients of terms of binomial theorem of positive and negative powers of \(n\) and \(-n\). This slows the process of producing the series of any particular trinomial expansion. This study established Kifilideen coefficient tables for positive and negative powers of \(n\) and \(-n\) of the Kifilideen trinomial theorem and other developments based on matrix and standardized methods. A Kifilideen theorem of matrix transformation of the positive power of \(n\) of trinomial expression in which three variables \(x,y\), and \(z\) are found in parts of the trinomial expression was originated. The development would ease evaluating the trinomial expression’s positive power of \(n\). The Kifilideen coefficient tables are handy and effective in generating the coefficients of terms and series of the Kifilideen expansion of trinomial expression of positive and negative powers of \(n\) and \(-n.\)

The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor’s classical theorem is often needed, but only tacitly assumed. In this note, we provide an elementary proof of this measurable Taylor’s theorem, which guarantees that the interpolating point in the Lagrange form of the remainder can be chosen to depend measurably on the independent variable.