# 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

### Pseudospectrum and condition pseudospectrum of non-archimedean matrices

JPRM-Vol. 18 (2022), Issue 1, pp. 75 – 82 Open Access Full-Text PDF
Abdelkhalek El Amrani, Jawad Ettayb, Aziz Blali
Abstract: In this paper, we introduce and study the notions of pseudospectrum, condition pseudospectrum of non-archimedean matrices and pseudospectrum of non-archimedean matrix pencil. Many results are proved and we give some examples.

### Complex Bipolar Fuzzy Soft Expert Sets

JPRM-Vol. 18 (2022), Issue 1, pp. 60 – 74 Open Access Full-Text PDF
Abd Ulzeez Alkouri
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.

### An Introduction to Soft Hypergraphs

JPRM-Vol. 18 (2022), Issue 1, pp. 43 – 59 Open Access Full-Text PDF
Bobin George, Jinta Jose, Rajesh K. Thumbakara
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.

### 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.