# Journal of Prime Research in Mathematics

Journal of Prime Research in Mathematics (JPRM) ISSN: 1817-3462 (Online) 1818-5495 (Print) is an HEC recognized, Scopus indexed, open access journal which provides a plate forum to the international community all over the world to publish their work in mathematical sciences. JPRM is very much focused on timely processed publications keeping in view the high frequency of upcoming new ideas and make those new ideas readily available to our readers from all over the world for free of cost. Starting from 2020, we publish one Volume each year containing two issues in June and December. The accepted papers will be published online immediate in the running issue. All issues will be gathered in one volume which will be published in December of every year.

Latest Published Articles

### The nonlinear time-fractional differential equations with integral conditions

JPRM-Vol. 17 (2021), Issue 2, pp. 168 – 181 Open Access Full-Text PDF
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.

### Some Integral Inequalities in the Framework of Conformable Fractional Integral

JPRM-Vol. 17 (2021), Issue 2, pp. 159 – 167 Open Access Full-Text PDF
Sikander Mehmood, Mariam Shahzad, Kiran Batool, Nawal Fatima, Juan E. N´apoles Vald$$^´$$es
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.

### Isomorphism Theorems in Generalized d−algebras

JPRM-Vol. 17 (2021), Issue 2, pp. 149 – 158 Open Access Full-Text PDF
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.

### Computation of Topological Indices for Inner Dual Graph of Honeycomb and Graphene Network

JPRM-Vol. 17 (2021), Issue 2, pp. 138 – 148 Open Access Full-Text PDF
FM Bhatti, Iqra Zaman, Sawaira Sikander
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.

### A Conceptual Framework of Convex and Concave Sets under Refined Intuitionistic Fuzzy Set Environment

JPRM-Vol. 17 (2021), Issue 2, pp. 122 – 137 Open Access Full-Text PDF
Abstract: Intuitionistic fuzzy set deals with membership and non-membership of a certain element of universe of discourse whereas these are further partitioned into their sub-membership degrees in refined intuitionistic fuzzy set. This study aims to introduce the notions of convex and concave refined intuitionistic fuzzy sets. Moreover, some of its important properties e.g. complement, union, intersection etc. and results are discussed.

### Correction on General Convergence Analysis for Two-Step Projection Methods and Applications to Variational Problems

JPRM-Vol. 18 (2022), Issue 1, pp. 38 – 42 Open Access Full-Text PDF
Abstract: The aim of this study is to illustrate that the main result of the paper [1] is incorrect by giving an counterexample. I also present and study a new algorithm 4.1 to correct the main result of [1]. The possible impact of this study is rather important, it puts a question mark on results in all references that have been cited This publication ( 203 times just in Google Scholar alone).