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

A Lower Bound for the First Hyper-Zagreb Index of Trees with given Roman Domination Number

JPRM-Vol. 21 (2025), Issue 1, pp. 49 – 54 Open Access Full-Text PDF
W. Ali, M. N. Husin
Abstract: In graph theory, the first Hyper-Zagreb index HM1(G) is calculated by summing the squares of the degrees of adjacent vertices u and v in molecular graphs. A Roman dominating function (RDF) on a graph G is a function z : V(G) → {0, 1, 2}, where V(G) is the vertex set, with the requirement that for each vertex v with z(v) = 0, there exists an adjacent vertex u such that z(u) = 2. The Roman domination number (RDN) denoted as ζR(G) and represents as the minimum total weight of all vertices under an RDF, and it plays a significant role in network analysis. In this paper, we present a new lower bound for the HZ1(T ) for trees T with order n and ζR(T ). These findings enhance our understanding of tree structures, providing chemists with a valuable tool for analyzing molecular stability and reactivity. By establishing mathematical bounds on the HZ1(T ), this research supports more precise predictions of molecular properties and aids in efficient experimental planning in chemical graph theory.
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Exponential (h,m)-Convex Functions, Basic Results and Hermite-Hadamard Inequality

JPRM-Vol. 21 (2025), Issue 1, pp. 40 – 48 Open Access Full-Text PDF
Muhammad Ajmal, Muhammad Rafaqat
Abstract: This paper explores the extension of the Hermite-Hadamard inequality to exponential (h,m)-convex functions, particularly within the framework of Caputo fractional integrals. Traditional calculus often falls short in adequately modeling systems with memory and non-local interactions, which are prevalent in various scientific and engineering fields. By incorporating Caputo fractional calculus, this work addresses complex dynamic systems that exhibit memory effects, a common characteristic in materials science, financial mathematics, and thermal physics. We present a series of new theoretical results including basic properties and integral inequalities of exponential (h,m)-convex functions, alongside their fractional counterparts. Further, we provide rigorous proofs of the Hermite-Hadamard inequality in both classical and fractional settings, demonstrating its utility in estimating bounds for real-world applications. The paper concludes with a detailed discussion on the practical implications of these findings in optimizing financial models, designing advanced materials, and engineering efficient thermal systems. Our results not only extend the classical understanding of convexity and its applications but also pave the way for future research in fractional calculus and its integration into applied mathematics.
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On a class of abstract fourth-order differential equations set on cusp domain

JPRM-Vol. 21 (2025), Issue 1, pp. 22 – 39 Open Access Full-Text PDF
Naceur Cheghloufa, Belkacem Chaouchi, Marko Kostic’, Fatiha Boutaous
Abstract: In this work, we concentrate on a boundary value problem set on a singular domain containing a cuspidial point. In our study, we obtain some existence and maximal regularity results. Our strategy is based on the study of a boundary value problems for a class of the complete abstract fourth-order differential equations involving fractional powers of unbounded linear operators.
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Deterministic and stochastic approaches for a fat receptor-breast cancer model with crossover effects

JPRM-Vol. 21 (2025), Issue 1, pp. 1 – 21 Open Access Full-Text PDF
Maroua Amel Boubekeur
Abstract: In this paper, the dynamics of a fat receptor-breast cancer model have been investigated by employing the deterministic and stochastic approaches. The existence of the endemic equilibrium, positivity of solutions and the calculation of the reproduction number are examined for the deterministic model and also the existence uniqueness of the stochastic model is discussed. Then, we will examine the crossover tendencies of the deterministic-stochastic model with the help of piecewise differential operators that take into account stochastic and power law processes followed by generalized Mittag-Leffler functions have been investigated. We employ a numerical scheme based on Newton polynomial to solve the deterministic-stochastic tumor growth model with fractional differential operators numerically. The graphical representations are simulated for different values of fractional order and the crossover tendencies of the deterministic-stochastic model are observed during the simulations.
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Insights into dual Rickart modules: Unveiling the role of second cosingular submodules

JPRM-Vol. 20 (2024), Issue 2, pp. 117 – 124 Open Access Full-Text PDF
M. Khudhair Abbas, Y. Talebi, I. Mohammed Ali
Abstract: In this paper, we propose a new type of module by focusing on the second cosingular submodule of a module. We define a module M as weak T-dual Rickart if, for any homomorphism φ ∈ EndR(M), the submodule φ(Z̄2(M)) lies above a direct summand of M. We prove that this property is inherited by direct summands of M. We also introduce weak T-dual Baer modules and provide a complete characterization of such modules where the second cosingular submodule is a direct summand. Furthermore, we present a characterization of (semi)perfect rings in which every (finitely generated) module is weak T-dual Rickart.
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Generalized Graph Energies of a Regular Graph under Vertex Duplication Operation

JPRM-Vol. 20 (2024), Issue 2, pp. 93 – 116 Open Access Full-Text PDF
Arooj Ibrahim, Saima Nazeer
Abstract: We provide a thorough examination of the graph energies in regular graphs that arise from the vertex duplication process in this paper. Understanding the numerous structural components of graphs requires understanding the thought of graph energy, known as a measurement obtained by computing eigenvalues the adjacency matrix of a graph. We derived generalized closed-form expressions for a number of important energy metrics, such as minimum degree, energy maximum degree energy, first Zagreb energy, second Zagreb energy and degree square sum energy, utilizing proficient algebraic graph theory techniques and eigenvalue spectrum analysis. Our work emphasizes on vertex duplication techniques and the impact they have on these energy metrics, primarily on regular graphs, a basic class of graphs where every vertex has the same degree. The resulting formulations offer further explanations for the behavior and attributes of these energy functions within the framework of regular graphs, providing a more comprehensive knowledge of how these operations affect the structural complexity of the graph. These findings greatly expand the conceptual model of graph energy and have potential uses in fields like combinatorics, chemistry, and network analysis where the energy models of graphs are extensively employed.
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Volume 21 (2025)

Volume 20 (2024)

Volume 19 (2023)

Volume 18 (2022)

Volume 17 (2021)

Volume 16 (2020)

Volume 15 (2019)

Volume 14 (2018)

Volume 13 (2017)

Volume 12 (2016)

Volume 11 (2015)

Volume 10 (2014)

Volume 09 (2013)

Volume 08 (2012)

Volume 07 (2011)

Volume 06 (2010)

Volume 05 (2009)

Volume 04 (2008)

Volume 03 (2007)

Volume 02 (2006)

Volume 01 (2005)