International Journal of Mathematics And its Applications

Blood Flow Through Stenosed Arteries in the Presence of Silica $(SiO_2)$ Nano Particles

Nitin. S. Bodke — 2025-12-31

The numerical investigation of blood flow through stenosed human arteries in the presence of Silica $(SiO_2)$ nanoparticles (NPs) is carried out. The governing equations are discretized using the finite difference method, and the simulations are performed in MATLAB. The study focuses on analyzing the influence of Silica $(SiO_2)$ nanoparticles on velocity distribution, volumetric flow rate, and resistive impedance. Results indicate that the inclusion of nanoparticles significantly alters these hemodynamic parameters, with a marked impact on velocity, flow rate, and impedance.

Analyzing Complexities in Decision-Making using Rough Intuitionistic Fuzzy Diagraphs

Kamesh Kumar — 2026-01-01

This research article introduces a hybrid approach which integrates a rough set with an intuitionistic fuzzy set. A rough intuitionistic fuzzy architecture is formed to study the vagueness, incompleteness, and ambiguity based information systems in some real life problems by using this hybridization. This study basically extends the existing rough fuzzy hybrid approach by generalizing some of its definitions and theorems. Finally, application of the proposed hybrid mechanism to decision-making problems underscores the potential of our method. Present article provides an efficient and effective tool for dealing complexities in decision-making. In particular, an efficient algorithm is developed to solve decision-making problem. Time complexity of proposed algorithm is also computed.

Hilbert Graceful Labeling on the Eight Sprocket Graph

J. Suresh Kumar — 2026-01-01

Let $ G $ be a simple, finite, connected, undirected, non-trivial graph with $ p $ vertices and $ q $ edges. Let $ V(G) $ be the vertex set and $ E(G) $ be the edge set of $ G $. The $ n^{\text{th}} $ Hilbert number is denoted by $ H_n $ and is defined by $H_n = 4(n - 1) + 1, \quad \text{where } n \ge 1$. A \emph{Hilbert graceful labeling} is an injective function $H : V(G) \rightarrow \{x : x = 4(i - 1) + 1, \, 1 \le i \le 2q\}$ which induces a bijective function $H^* : E(G) \rightarrow \{1, 2, 3, 4, \ldots, q\}$ defined by $H^*(uv) = \frac{1}{4} \, |H(u) - H(v)|$, $\forall \, uv \in E(G), \, u, v \in V(G)$. A graph that admits a Hilbert graceful labeling is called a \emph{Hilbert graceful graph}. This paper focuses on the Eight Sprocket Graph $ SC_n $ and demonstrates its Hilbert gracefulness. It also investigates related graph families formed from copies of $ SC_n $, proving that the path union, cycle, and star of the Eight Sprocket Graph are all Hilbert graceful.

On the Stability of the Quadratic Functional Equation $f(2x+y) + f(x+2y)$ $= 4f(x+y) + f(x) + f(y)$ in $2$-Banach Space

Bhavin Mansukhlal Patel — 2026-01-01

In this research paper, we investigate the Hyers-Ulam stability of the functional equation $f(2x+y) + f(x+2y) = 4f(x+y) + f(x) + f(y)$ in $2$-Banach space.

Fixed Point Theorem of Generalized Contraction for Multi-valued Mapping on Fuzzy Metric Spaces

Arjun Singh Yadav — 2026-01-01

We prove a Generalized type fixed point theorem for multi-valued mappings on G-complete fuzzy metric spaces. The proof uses the Hausdorff fuzzy metric space which was introduced by Rodriguez-Lopez and Romaguera \cite{Lopez}. We also generalized previous known results.

Application of m-Ranking to Node Analysis in Complex Networks

Shibu Manuel — 2026-01-01

Identifying influential nodes in complex networks has gained considerable attention because of its significant theoretical importance and broad range of applications. The m-Ranking method incorporates both the degree of nodes and the weights of edges to rank nodes with varying importance levels. This approach can also be applied to unweighted networks by simply setting the weight parameter $\alpha= 1$. Furthermore, we illustrate the effectiveness of the proposed method using a real-world air traffic network, where the rankings produced are shown to be more meaningful compared to those obtained through existing methods.

Multifactor Balanced Asymmetrical Factorial Designs of Type III

N. J. Wanyoike — 2026-01-08

This manuscript gives a method of constructing multifactor BAFDS of type III. Multi-factor BAFDS of type III are constructed from two factor BAFDS. The method was given by [21] and it generates a BAFD from two given BAFD's. The method can provide efficient BAFD's if efficient two factor BAFD's are used. The designs constructed are balanced with orthogonal factorial structure.

Some Common Fixed Point Results in $b-$metric Spaces Endowed with a Graph

Luwen Miao — 2026-01-25

In this paper, we study the conditions for the existence of a unique common fixed point of generalized $(\psi,\varphi)-$ contractive mappings in the framework of $b-$metric spaces endowed with a graph. We give some examples to support our results.

Certain Curvature Conditions on $N(k)$-Contact Metric Manifold

Gajendra Nath Tripathi — 2025-01-25

We consider a concircularly semi-symmetric $N(k)$-contact metric manifold and we classify $N(k)$-contact metric manifolds satisfying the curvature conditions $\widetilde{Z}.S = 0$, $Q.\widetilde{Z} = 0$, $\widetilde{Z}.P = 0$.

Eccentric Degree Connectivity Index of Graphs

Veena Mathad — 2025-01-25

In this paper, a novel eccentric degree based topological index termed as eccentric degree connectivity index is conceptualized. For a connected graph $G$ with a vertex set $V$, the eccentric degree connectivity index denoted by $\xi^{ed}$ is defined as $\xi^{ed}=\displaystyle\sum_{v\in V}ed(v)e(v)$. We obtain it's value for some classes of graphs and graph operations namely, join, corona, corona join, $r-$crown graph of fan graph and $r-$crown graph of wheel graph. We also derive some upper and lower bounds.

An Extension of the Compression-Expansion Fixed Point Theorem of Functional Type

Sulekha Tomar — 2026-01-25

In this article we use an interval of functional type as the underlying set in our compression-expansion fixed point theorem argument which can be used to exploit properties of the operator to improve conditions that will guarantee the existence of a fixed point in applications. An example is provided to demonstrate how intervals of functional type can improve conditions in applications to boundary value problems. We also show how one can use suitable $k$-contractive conditions to prove that a fixed point in a functional-type interval is unique.

Common Fixed Point Theorems in Modular Multi-Metric Spaces

Rahul S. More — 2025-01-25

In this paper, we study the existence and uniqueness of common fixed points for compatible self-mappings in modular multi-metric spaces, which generalize both modular and multi-metric spaces. We introduce contractive conditions suitable for this setting and establish a common fixed point theorem that extends classical results such as Banach’s contraction principle and Jungck’s theorem. An illustrative example is provided to demonstrate the applicability of the main result. The results contribute to the theory of fixed points in spaces with multiple modular structures and offer potential applications in nonlinear analysis and optimization.

Bessel Type Function $J^{\theta}_{\beta}$, Bessel Type Operator $\Delta^{\theta}_{\beta}$ and Fractional Fourier-Bessel Type Transform $\mathcal{F}^\theta_{\beta}$

Abhisekh Shekhar — 2026-01-29

Fractional Fourier-Bessel type transformation is defined. Then using these transformations the pseudo-differential Bessel type operators $\mathscr{B}^{\theta}_{\beta,~a}$ is also defined. After that we introduce some class of symbols, Sobolev and Bessel type potentials spaces. Properties of these transformations and operators are investigated.