Journal of Computational Mathematica

Bivariate Optimal Replacement Policies under Partial Product Process for Multistate Degenerative Systems

Affan Ahmed J — 2026-06-15

In this paper, we consider on a multistate degenerative system with k working states and l-failure states and study the maintenance problems under various bivariate replacement polices (T, N),(T +, N),(U, N),(U −, N). The long-run average cost of a multistate degenerative system is calculated. Under the afore-mentioned bivariate replacement policies under partial product process optimality in inferred. In this study, the results developed are strengthened with numerical examples.

Generalization of Product Cordial Magic and Super Mean Labeling on Three Dimensional Graph and its Applications

Sudhakar V — 2026-06-15

A Graphical representation of a graph are labeled by positive integers then the resultant graph is a r-regular graph. In this paper we introduce a product of two multi magic labeling on any r- regular graph and magic Petersen graph was introduced. Applications of magic Petersen graph and product of two multi magic labeling are also dealt in this research article.Well defined three dimensional cubic graphs are taken for initializing the new labeling called product of magic labeling.

AMGL Coding Technique on Felicitous Labeling of Braid Graphs and its Applications

Leena S — 2026-06-15

Graph labeling plays a vital role in modern graph theory due to its wide range of applications in communications networks, cryptography, and coding theory. Among various labeling schemes, felicitous labeling is significant because of its modular arithmetic structure and uniqueness of edge labels. In this paper, the braid graph B(n) is studied under felicitous labeling and is further utilized for developing an efficient AMGL (Alphabets Maneuvered Graph Labeling) coding algorithm, and computational implementations are presented. Experimental results show that braid graphs provide a strong framework for secure message encoding and decoding. The study highlights the effectiveness of braid graphs in bridging mathematical theory with practical coding applications.

Higher-Order Generalized q-Difference Equations and Lucas-Type Series Solutions via Inverse q-Difference Operators

Divya Bharathi S — 2026-06-15

In this paper, we introduce and analyze a novel class of t^th-order generalized q-difference equations associated with multi-parameter recurrence relations. By employing an inverse q-difference operator framework, explicit solution representations are derived in terms of generalized Lucas-type sequences. A higher-order Lucas series formula is established, providing closed-form summation identities for polynomial and logarithmic forcing functions. Several corollaries illustrate the effectiveness of the proposed method, including quadratic and logarithmic source terms. The obtained results extend classical Fibonacci-Lucas summation techniques to higher-order q-calculus and unify discrete summation identities within a single operator-theoretic setting. The proposed framework offers a systematic approach for solving higher-order q-difference equations and paves the way for further developments in fractional q-difference equations, discrete dynamical systems, and applications involving special sequences.

Optimization of Transportation Cost Using Least Cost Method and Vogel’s Approximation Method Implemented in Python

Bhuvaneshwari R — 2026-06-15

Transportation problems are a fundamental class of optimization problems in Operations Research that aim to minimize the cost of distributing goods from multiple supply locations to multiple demand locations. Efficient allocation strategies are required to reduce operational costs and improve logistics performance. This study presents the implementation of two classical techniques used to obtain an initial feasible solution to transportation problems: the Least Cost Method (LCM) and Vogel’s Approximation Method (VAM). The algorithms are implemented using Python to automate computations and reduce manual calculation complexity. A comparative analysis is conducted using a dataset consisting of multiple supply and demand nodes. The results show that Vogel’s Approximation Method produces solutions that are closer to the optimal transportation cost compared to the Least Cost Method. The study highlights how computational tools can improve decision-making in logistics and supply chain management.

Linear Programming and North-West Corner Method for Transportation Optimization Using Python

Hemavathy P — 2026-06-15

Efficient resource allocation and transportation planning are essential components of industrial decision-making. Linear Programming (LP) is widely used to optimize resource utilization by maximizing profit or minimizing cost under certain constraints. The North-West Corner Method (NWCM) is a simple technique used to obtain an initial feasible solution to transportation problems. This study presents the implementation of Linear Programming and the North-West Corner Method using Python programming. A manufacturing-based case study is considered to demonstrate how optimization techniques assist organizations in production planning and transportation scheduling. The results show that Python-based optimization models can efficiently determine optimal production levels and feasible transportation allocations. The study highlights the practical importance of computational optimization techniques in modern supply chain and manufacturing systems.

Bifurcation from a Stable Equilibrium in the Genome

Geethalakshmi S — 2026-06-15

This work explores a genome network and introduces the concepts of core and layering within the network. Based on this structure, a dynamical system for gene expression levels is developed. The system exhibits two main bifurcations arising from a stable equilibrium. Preliminary results toward understanding these bifurcations in n-dimensions are also presented. This work contributes to a deeper understanding of genome dynamics and controllability.

On Domination in Path, Cycle, Star, Wheel and Grid Graphs

Velmurugan N — 2026-06-15

Domination is one of the important concepts in graph theory with applications in communication networks, facility location problems and social network analysis. In this paper we study domination numbers for several basic graphs including path graphs, cycle graphs, star graphs, wheel graphs and grid graphs. Exact formulas for domination numbers are obtained and relationships between different classes of graphs are discussed. Illustrative examples, tables and diagrams are provided.

Application of Dynamic Programming Technique to Reliability Model in Space Mission

Preetha S — 2026-06-15

The research demonstrates how dynamic programming can be used to improve the reliability of space mission systems. Spacecraft systems require traditional reliability models to operate because their multiple interdependent subsystems face three strict boundaries of cost, weight and power. This method helps the system in modelling as a multistage decision process, applying optimal redundancy at each stage and maximizing the mission success probability. In this paper the recursive relation method is applied to determine the most efficient subsystem configuration based on available resources. A numerical example demonstrates how effective the technique functions. The study concludes that dynamic programming provides a systematic and efficient framework for enhancing reliability in complex, high-risk space missions.

Existence, Stability, and Numerical Analysis of a Caputo Fractional Population Model

Jenitha Borges M — 2026-06-15

Fractional-order population models have attracted considerable attention due to their capability to describe memory-dependent biological processes more effectively than classical integer-order systems. Motivated by the limitations of traditional population growth equations in capturing hereditary effects, this paper investigates a fractional logistic population model formulated in the Caputo sense. The proposed model incorporates nonlocal memory characteristics, which play an important role in realistic biological and ecological systems. Analytical properties of the model are studied by establishing existence and uniqueness results through fixed point theory. In addition, equilibrium analysis and asymptotic stability conditions are derived for the fractional-order system. The study further demonstrates how the fractional parameter influences the growth dynamics and convergence behavior of the population. Numerical simulations and graphical illustrations are presented to validate the theoretical findings and to compare the fractional and classical models. The obtained results indicate that the Caputo fractional framework provides a more flexible and generalized approach for modeling population evolution with memory effects. The proposed methodology may also be extended to epidemic systems, predator-prey interactions, and other nonlinear biological models governed by hereditary phenomena.

Fractional Optimal Control of a Riemann-Liouville Tumour Growth Model with Chemotherapy Effect

Jenitha Borges M — 2026-06-15

This paper investigates a fractional optimal control problem for tumour growth dynamics governed by a Riemann-Liouville fractional differential equation. The proposed formulation incorporates chemotherapy treatment as a time-dependent control function within a nonlinear memory-dependent state system. A quadratic cost functional is introduced to balance tumour suppression and drug toxicity. The novelty of this work lies in the integration of Riemann-Liouville fractional dynamics with an optimal chemotherapy control strategy in a unified framework. Existence of admissible solutions is established using fixed-point arguments, while necessary optimality conditions are derived via a fractional Pontryagin maximum principle. Numerical simulations are presented to illustrate the effectiveness of the control strategy and to analyze the influence of the fractional order on treatment performance. The results demonstrate that fractional-order dynamics provide a more flexible framework for capturing memory-dependent tumour response under chemotherapy.