M-polynomial of chemical compounds is a recent idea and it produces closed forms of many degree-based topological indices which correlate chemical properties of material under investigation. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules like boiling point, stability, strain energy etc. are correlated with their structures. In this paper, we determine general closed formulae for M-polynomials of the Sierpinski graph. We recover important topological degree-based indices. We also give different graphs of topological indices and their relations with the parameters of structures.

Topological indices are real numbers associated with molecular graphs and catch symmetry of molecular structures that give it a scientific dialect to foresee properties. In this work, we compute first and second reverse Zagreb indices, first and second reverse hyper Zagreb indices, reverse Atomic-bond connectivity index and reverse Geometric-arithmetic index for TUC₄[m, n].

In this paper, we investigate the system undergoes flip and Neimark Sacker bifurcation in the interior of R ₊ ² by using the center manifold theorem and bifurcation theory. The dynamics of this discrete time predator-pre model is investigated in the closed first quadrant of R ₊ ² .

In this paper, we define a new function, namely, harmonically α , h − m -convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér–Hadamard fractional integral inequalities for harmonically α , h − m -convex functions via generalized fractional integral operators are proved. From presented results, a series of fractional integral inequalities can be obtained for harmonically convex, harmonically h − m -convex, harmonically α , m -convex, and related functions and for already known fractional integral operators.

The theory of rough sets is successfully applied in various algebraic systems (e.g. groups, rings, and modules). In this paper, the concept of roughness is introduced in modules of fractions with respect to its submodules. Hence, the notion of the lower and upper approximation spaces based on a submodule of the modules of fractions is introduced. Some fundamental results related to these approximation spaces are examined with examples. Moreover, this paper establishing several connections between the approximation spaces of two different modules of fractions with respect to the image and pre-image under a module homomorphism. This technique of building up a connection among the approximation spaces via module homomorphisms is useful to connect two information systems in the field of information technology.

This paper aims to obtain the bounds of a class of integral operators containing Mittag–Leffler functions in their kernels. A recently defined unified Mittag–Leffler function plays a vital role in connecting the results of this paper with the well-known bounds of fractional integral operators published in the recent past. The symmetry of a function about a line is a fascinating property that plays an important role in mathematical inequalities. A variant of the Hermite–Hadamard inequality is established using the closely symmetric property for $(\alpha ,m)$-convex functions.