International Journal of Mathematics And its Applications

Generalized Fractional Integral Operators and Special Functions

2025-07-09T05:03:42+00:00

In the present paper, we established some composition formulas Marichev-Saigo-Maeda (MSM Fractional Calculus Operator & MSM Fractional Differential Operators), then studied about some functions like Lerch Transcendent Function, Bessel Functions from various research papers and applied them to these integral operators and get some new results.

A Graph Theoretic Analysis of Leverage Eccentricity Centrality

2026-01-10T13:08:35+00:00

In complex networks, the identification of key regions is determined through centrality measures. There are various centrality measures in which leverage centrality is specially designed for neural network. The concept of leverage centrality is the relationship between degree of a vertex relative to its neighbours and it operates under the principle that a vertex in a network is central if its immediate neighbours rely on it for information. In this paper, we built upon leverage centrality and introduce leverage eccentricity centrality, which is a measure of how eccentricity of a vertex rely on the eccentricity of all its neighbours. We investigate this property from a mathematical perspective. We first outline some of the basic properties and then compute leverage eccentricity centrality of vertices in different families of graphs, line graph of some special graphs, Mycielskian of some standard graphs, and molecular graph of cyclo-hydrocarbons.

Dynamical Modelling for Epidemics of Vector Transmitted Diseases With Non-Monotone Incidence

2026-01-31T16:01:14+00:00

This paper presents a mathematical formulation for vector-host disease dynamics in which the transmission process is governed by incidence functions with non-monotone characteristics. The study investigates how changes in the behavior of susceptible hosts influence infection levels, alongside examining the role of vector deterrents in modifying vector infection dynamics. The long-term behavior of the system is analyzed by establishing the global asymptotic stability of equilibrium states using suitably constructed Lyapunov functionals. To support the analytical conclusions, numerical simulations are carried out. The proposed framework provides a clearer understanding of the mechanisms driving the spread of vector-borne infections.

The m-Ranking of Nodes in Weighted Networks

2026-03-21T17:31:11+00:00

Identifying pivotal nodes within complex systems has emerged as a cornerstone of network science, offering both profound theoretical insights and significant practical utility. However, only a limited number of centrality measures are applicable to weighted networks. Addressing this limitation, the m-Ranking method has been introduced as a robust analytical framework that evaluates node hierarchy by integrating connection density with the specific intensity of link weights. This approach is notably versatile and maintains high precision in weighted network environments.

$\rho-$Statistical Convergence of Order $\alpha$ in Partial Metric Spaces

2026-03-21T17:36:20+00:00

In the present study, we introduce and study the notions of $\rho-$statistically convergence and $\rho-$statistically boundedness of order $\alpha$ in a partial metric space $(X,p)$ and a relation between these two concepts is established, where $\rho=(\rho_n)$ is a non decreasing sequence of positive real numbers. Apart from this, we explored the inclusion relations between $\rho-$statistical convergence and $\rho-$statistical boundedness with the variation of the sequence $\rho=(\rho_n)$.

Transportation Problem of Multi-objective Multi-item Solid Using Fuzzy Environment

2026-03-21T17:42:26+00:00

The transportation issue pertains to the reservation of fully loaded vehicles, which may include light commercial vehicles, medium-duty trucks, and heavy-duty trucks, among others. The transportation costs are incurred irrespective of whether the vehicle's capacity is fully utilized. Moreover, instead of transporting a single item, it may be essential to transfer various types of items from multiple sources to different destinations utilizing a variety of conveyances. The optimal transportation approach can be affected by several factors, such as the volume and weight of each product unit, as well as the insufficient availability of a sufficient number of specific vehicle types. This paper introduces a formulation of a multi-objective, multi-item solid transportation problem that considers all these factors. The problem is characterized by transportation cost and time parameters that are treated as fuzzy variables. By utilizing the credibility theory of fuzzy variables, a chance-constraint programming model is created and subsequently transformed into its deterministic equivalent. Lastly, a numerical example is included to illustrate the problem.