Journal of Prime Research in Mathematics

Abstract: The idea of representing information with its periodic nature has been extensively studied and applied in many fields. Many researchers have developed several tools to transfer uncertainty information that has the same data but with different meanings that happening in different phases/times. The novelty of combining complex numbers and uncertainty information appears in its ability to represent two values uncertainty and periodicity semantics in one mathematical tool. In this paper, we generalize existence concept of bipolar fuzzy soft expert sets (BFSES) from real number to complex numbers to be complex bipolar fuzzy soft expert sets (CBFSES). This generalization allows us to convey data that carry benefits, features, and specifications of BFSES in different phases or carrying periodic nature of the BFSE information to mathematical formula and vice versa without losing full meaning of information. The range of value becomes to be in unit disk in a complex plane for both positive and negative membership functions of BFSES. The main benefit of CBFSES that amplitude and phase terms can convey bipolar fuzzy information. Moreover, formal definition of CBFSES and illustration examples are introduced. Also, we define basic operations and their properties on CBFSES. Finally, OR and AND operations are generalized to the form of CBFSES.

Abstract: This is an introductory paper on Soft Hypergraph. In 1999, D. Molodtsov initiated the concept of soft set theory. This is an approach for modeling vagueness and uncertainty. The concept of soft graphs introduced by Rajesh K. Thumbakara and Bobin George is used to provide a parameterized point of view for graphs. Theory of soft graphs is a fast developing area in graph theory due to its capability to deal with the parameterization tool. Hypergraph is a generalization of graph. In this paper we introduce the concept of soft hypergraph by applying the idea of soft set in hypergraph. By means of parameterization, soft hypergraph produces a series of descriptions of a relation described using a hypergraph.

Abstract: In this paper, we present a nonlinear equation modeling a time-fractional pseudoparabolic problem, involving fractional Caputo derivative where the fractional order is 0 < α < 1. We first started with the associated linear problem, we establish the energy inequalities to obtaine a priori estimate,and demonstrate the density of the operator’s range generated. Accordingly, the existence and uniqueness of the weak solutions are given, then we use the preceding results to handle the nonlinear case via an iterative process.

Abstract: In this paper, we use new definition of left and right conformable fractional integral to obtain some new inequalities. The results obtained are refinements of existing results.

Abstract: We introduce the generalized d-algebras, generalized d-ideals (d∗-ideals, d#-ideals, d$-ideals) and other related notions. We also prove some properties about d-ideal, d#-ideal and results related to quotient generalized d-algebra. Through these constructions, we prove the first, second and the third isomorphism theorems for the generalized d-algebras. These developments contribute to the theory of the BCI/BCK/BCH and the generalized BCH-algebras.

Abstract: In QSPR/QSAR study, the molecular structure indices are now standard methods for studying structureproperty relations. Due to the chemical significance of these indices, the number of proposed molecular descriptors is quickly rising in the last few years. A topological index is a transformation of a chemical structure into a real number. In mathematics, honeycomb networks are widely used because of their extreme importance in computer graphics, image processing, cellular phone base stations, and in chemistry to represent benzenoid hydrocarbons. They are formed by recursively using hexagonal tiling in a particular pattern. HC(n) represents the honeycomb network of dimension n, where n is the number of hexagons between boundary and central hexagon. An atomic-scale honeycomb structure composed of carbon atoms is known as graphene. Professor Andre Geim and Professor Kostya Novoselov separated it from graphite in 2004. It is the first 2D material that is one million times thinner than human hair, two hundred times stronger than steel, and the world’s most conductive material. The graph 2D graphene is expressed as G(r, s) where “r” means the number of rows, and “s” is the number of hexagons in a row. This paper uses the inner dual graph of honeycomb networks and 2D graphene network, which are named as HcID(n) and GID(r, s) respectively. We derive some results related to topological indices for these graphs. We compute degree-based indices, first general Zagreb index, general Randi´c connectivity index, general sum-connectivity index, first Zagreb index, Second Zagreb index, Randi´c index, Atom-bond Connectivity (ABC) index, and Geometric-Arithmetic (GA) index of inner dual graphs of honeycomb networks and graphene network.