# 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

### Characterizations of Chevalley groups using order of the finite groups

JPRM-Vol. 16 (2020), Issue 1, pp. 46 – 51 Open Access Full-Text PDF
Abid Mahboob, Taswer Hussain, Misbah Akram, Sajid Mahboob, Nasir Ali, Ali Raza
Abstract: In this paper, we prove $$\psi (A_{1}(4))< \psi(G)$$, $$\forall$$ groups which are not simple with order sixty, $$A_{1}(4)$$ is Chevalley group (Linear group) of order 60. Also we prove that $$\psi (A_{2}(2))< \psi(G)$$ using higher order non-simple groups of order 168.

### Construction of optimal derivative free iterative methods for nonlinear equations using Lagrange interpolation

JPRM-Vol. 16 (2020), Issue 1, pp. 30 – 45 Open Access Full-Text PDF
Moin-ud-din Junjua, Saima Akram, Tariq Afzal, Ayyaz Ali
Abstract: In this paper, we present a general family of optimal derivative free iterative methods of arbitrary high order for solving nonlinear equations by using Lagrange interpolation. The special cases of this family with optimal order of convergence two, four, eight and sixteen are obtained. These methods do not need the Newton’s or Steffensen’s iterations in the first step of their iterative schemes. The advantage of the new schemes is that they are also extendable to the iterative methods with-memory. Numerical experiments and polynomiographs are presented to confirm the theoretical results and to compare the new iterative methods with other well known methods of similar kind.

### Fractional Optimal Control for a Corruption model

JPRM-Vol. 16 (2020), Issue 1, pp. 11 – 29 Open Access Full-Text PDF
Ebenezer Bonyah
Abstract: In this work, a fractional optimal control of corruption model is investigated. The variable controls are included in the model to optimize the best strategy in reducing the corruption in the society. The fraction derivative employed in the study is in Atangana–Beleanu–Caputo (ABC) sense based on generalized Mittag–Leffler. The uniqueness and existence of solution of the corruption model is established. The necessary and sufficient condition for establishing fractional optimal control in ABC sense is determined. A numerical algorithm for obtaining fractional optimal control solution is presented. The numerical solution results show that the best strategy in controlling corruption in the society is to optimize all the thee controls simultaneously.

### Some properties of the maximal graph related to co-ideal of a commutative semiring

JPRM-Vol. 16 (2020), Issue 1, pp. 1 – 10 Open Access Full-Text PDF
Yahya Talebi, Atefeh Darzi
Abstract: For a commutative semiring $$R$$ with non-zero identity, the maximal graph of $$R$$, denoted by $$MG(R)$$, is the graph whose vertices are all elements of $$UM(R)$$ with two distinct vertices joined by an edge when there is a maximal co-ideal that contains both of them. In this paper, we study some properties of maximal graph such as planarity, radius, splitting and domination number.

### Some new estimates of generalized $$(h_1, h_2)$$-convex functions

JPRM-Vol. 1 (2019), Issue 1, pp. 129 – 146 Open Access Full-Text PDF
Farhat Safdar, Muhammad Aslam Noor, Khalida Inayat Noor, Saima Rashid
Abstract: In this article, we introduce a new class of generalized convex functions involving two arbitrary auxiliary functions $$h_1, h_2 : I = [a, b] ⊆ R → R$$, which is called generalized $$(h_1, h_2)$$ convex functions. We obtain several new classes of convex functions as special cases. We derive some new integral inequalities for generalized convex functions. Several special cases are also discussed. Results proved in this paper can be viewed as new significant contributions in this area.

### Forgotten index of generalized F-sum graphs

JPRM-Vol. 1 (2019), Issue 1, pp. 115 – 128 Open Access Full-Text PDF
H. M. Awais, M. Javaid, M. Jamal
Abstract: Liu et al. [IEEE Access; 7(2019); 105479-105488] defined the concept of the generalized subdivided operations on graphs and obtained the generalized F-sum graphs. They also calculated the 1st and 2nd Zagreb indices of the generalized F-sum graphs. In the continuation of this work, we study the forgotten index (F-index) of the generalized F-sum graphs in terms of different topological indices (TI’s) of their base graphs. In the end, the results of F-index on the generalized F-sum graphs acquired by the particular classes of alkane are also included.