International Journal of Mathematics And its Applications

Existence of Common Coupled Fixed Points of a Pair of Operators

2026-06-13T09:17:21+00:00

In this paper, we continue on this path by investigating the existence of common coupled fixed points of a pair of operators $A,B: \Omega\times \Omega \rightarrow\Omega,$ where mixed monotone type properties of the operators are not assumed, while the pair of operators is assumed to satisfy a new two-dimensional order type property, extending a well-known one-dimensional equivalent property, and guaranteeing the use of monotone iterative technique. To prove the existence of a common coupled fixed point for such pair of operators, it is assumed for operators to satisfy a useful condensing and contractive conditions (conditions ($C_{1}$) and ($C_{2}$) hereafter) involving the two-dimensional setting.

Fixed Point Theorem and Applications to Systems of Hammerstein Type Integral Equations

2026-06-13T09:21:36+00:00

In this paper we present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of positive solutions for systems of nonlinear Hammerstein integral equations. An example is also presented to show the applicability of our results.

Fixed Point Theorems for Generalized Contraction in Semi-Metric Spaces With Triangular Functions

2026-06-13T09:27:09+00:00

This paper advances a line of research in fixed point theory initiated by M. Bessenyei and Z. P\'ales, building on their introduction of the triangle function concept in [15]. By applying this concept, the study revises several well-known fixed point theorems in metric spaces, extending their applicability to semimetric spaces with triangle functions. The paper focuses on general theorems involving weak, partial, Bianchini and Chatterjea-Bianchini contractions, deriving corollaries relevant to metric spaces, $b$-metric spaces, ultrametric spaces, and distance spaces with power triangle functions. Notably, several new and interesting findings emerge in the context of weak and partial contractions.

Application of Perove Type Fixed Point Theorem in Vector Valued $B$-Metric Spaces

2026-06-13T09:30:28+00:00

In this paper, we extended the definition of $ b $-metric spaces to encompass the vectorial scenario, wherein the distance is represented as a vector, and the constant in the triangle inequality axiom is substituted with a matrix. For these spaces, we present findings that are similar to those in the $ b $-metric framework: fixed-point theorems, stability results, and a version of Ekeland's variational principle. Consequently, we also obtain a variation of Caristi's fixed-point theorem.

Monotonic Behavior in Subdiffusion Equation of the Parameter in Mittag-Leffler Function

2026-06-13T09:33:39+00:00

In this paper, we demonstrate the strict monotonicity concerning the parameter $ ho$ of the Mittag-Leffler functions $E_ ho(-t^ ho)$ and $t^{ ho -1}E_{ ho, ho}(-t^ ho)$. Furthermore, the results obtained are applicable to a broader class of subdiffusion equations than those previously examined.

Improvement of Exponential Chain-Type Estimators of Population Mean Under Double Sampling

2025-12-05T06:33:00+00:00

Three exponential chain-type regressions, ratios, and population-average regression estimators utilising information from two auxiliary variables under double sampling are proposed in this study. Up to the first approximation order, details of behaviours are performed with bias and average square errors in mind. We compared it to other popular chain type estimating systems of the same kind and offered survey professionals some suggestions on how to improve their own methods.

Degcity Indices of Some Networks

2026-03-05T13:27:25+00:00

Topological indices are important tools for analyzing structural properties of graphs and interconnection networks. In this paper, we compute seven eccentricity-based degcity indices for honeycomb, oxide, and hypertree networks. By employing edge partition techniques based on vertex degree and eccentricity, explicit formulae are derived for each network class. The results contribute to the theoretical study of degree-eccentricity interactions and provide useful descriptors for the analysis and design of complex network structures.

Effect of Chemical Reaction on Heat and Mass Transfer in MHD Rotating Flow of a Couple Stress Fluid through a Porous Medium with Temporal Oscillatory Permeability

2026-01-30T09:44:11+00:00

The present investigation focuses on the analysis of heat and mass transfer characteristics in an unsteady free convective magnetohydrodynamic (MHD) rotating flow of a couple-stress fluid past a vertical porous plate embedded in a porous medium. The study incorporates the effects of time-dependent oscillatory suction and permeability, along with the presence of an internal heat generation source and a first-order homogeneous chemical reaction. The influence of an externally applied transverse magnetic field is also taken into account to examine its role in controlling the flow dynamics. The governing system of highly nonlinear partial differential equations describing the conservation of momentum, energy, and species concentration is formulated under appropriate physical assumptions. These equations are rendered dimensionless using suitable similarity transformations and are subsequently decomposed into steady and oscillatory components to facilitate analytical treatment. The resulting coupled nonlinear differential equations are solved numerically using an efficient numerical scheme. A comprehensive parametric study is carried out to illustrate the effects of key dimensionless parameters, such as the magnetic field parameter, rotation parameter, couple-stress parameter, permeability parameter, heat source parameter, and chemical reaction parameter, on the velocity, temperature, and concentration distributions. The numerical results are presented graphically and discussed in detail to highlight the underlying physical mechanisms governing the flow behaviour. The findings of this study are expected to be useful in understanding complex transport phenomena in engineering and industrial processes involving non-Newtonian fluids, porous media, and MHD applications.

A Delayed Host-Parasite Model with Partial Host Cover and Parasite Harvesting

2026-02-27T04:53:37+00:00

This paper improves and investigates a delayed host parasite communication model that encompasses partial host cover and parasite harvesting. The partial cover represents a constant fraction of the host population that is temporarily shielded from parasitic attack due to behavioural, spatial, or physiological refuge. The delay accounts for the time lag in the parasites growing process or infection transmission. A system of nonlinear delay differential equations formulated to describe the population dynamics. The equilibria and their stability are examined, and analytical conditions for the occurrence of the Hopf bifurcation are derived. The results show that intensifying time delay can dislocate the positive equilibrium, ahead to periodic oscillations, whereas increasing host cover or harvesting strength has a steadying influence. The numerical simulations back up the theory and show just how complicated these systems can get. We see stable coexistence, ongoing oscillations, and even points where everything collapses. This study really shines a light on how delayed reactions, safe zones, and different harvesting strategies shape the long-term behaviour of host parasite relationships, passive implications for sustainable management and biological control.

Deformation in Orthotropic Elastic Media under the Effect of Triangular Irregularity

2026-01-27T15:39:48+00:00

Closed-form analytical expressions for displacements have been obtained using Eigen value approach and Fourier transform method in orthotropic media, considering the triangular irregularity in one medium. To study the effect of irregularity, two orthotropic materials-Olivine and Topaz have been used. The variation in displacements with respect to horizontal distance has been analyzed by considering the irregularities of different size.

Comparative Growth of Composite Entire and Meromorphic Functions and Wronskians Generated by them on the Basis of their $(\alpha ,\beta ,\gamma )$-order

2025-12-26T19:00:49+00:00

In this paper, we have established some results relating to the comparative growth properties of composite transcendental entire or meromorphic functions and Wronskians generated by one of the factors on the basis of $(\alpha ,\beta ,\gamma )$-order and $(\alpha ,\beta ,\gamma )$-lower order, where $\alpha ,\beta ,\gamma $ are continuous non-negative functions defined on $\left( -\infty ,+\infty \right) .$

Best Proximity Point Theorems for $d$-Rational Cyclic Contractions in Dislocated Metric Spaces

2025-10-10T08:19:41+00:00

In this work, we define $d$-rational cyclic contraction in the setting of dislocated metric space. Some existence and convergence results for best proximity points have been demonstrated. Further, illustrative examples are provided in the support of results proved.

Influence of Crack Depth on Stress Distribution in a Semi-Infinite Elastic Medium Under a Moving Load

2026-01-14T16:31:44+00:00

This study investigates the influence of crack depth on stress distribution in a semi-infinite elastic medium under a moving load. A buried Mode-III crack is considered at varying depths (0.1~m to 3.0~m), and the load moves with constant velocity ranging from 10~m/s to 50~m/s. Using Fourier transform techniques, the displacement and stress fields are derived. The results show that increasing crack depth significantly reduces surface stress and alters the stress distribution pattern. Validation with existing literature confirms model accuracy. This model is applicable to fault-line analysis and underground rail/road evaluations. A time-dependent stress analysis is also performed to highlight the dynamic interaction between moving loads and buried cracks, offering practical insights for subsurface infrastructure monitoring and failure prediction.

Magnetohydrodynamic Flow of a Couple-Stress Fluid Through a Non-Homogeneous Porous Medium with Oscillatory Suction and a Heat Source/Sink

2026-06-13T12:16:42+00:00

The present study investigates the heat and mass transfer characteristics of free convective flow of an incompressible, electrically conducting couple-stress fluid past a vertical porous plate embedded in a porous medium, in the presence of a uniform transverse magnetic field and internal heat source. The permeability of the porous medium and the suction velocity at the plate are assumed to vary periodically with time. The nonlinear governing partial differential equations describing the flow, thermal, and concentration fields are decomposed into steady and oscillatory components and subsequently reduced to a system of ordinary differential equations. An analytical solution is obtained using a regular perturbation technique. The effects of pertinent physical parameters on the velocity, temperature, and concentration distributions are examined and illustrated graphically, with particular emphasis on the influence of time-dependent suction and oscillatory permeability on the transport processes. The results demonstrate that periodic variations in permeability and suction significantly modify the flow structure as well as the thermal and solutal boundary layers of the couple-stress fluid. The results of this investigation are interesting for understanding transport phenomena in porous media with non-Newtonian fluids under periodically varying operating conditions.

Generalized Polygonal Sum Labeling of Some Families of Graphs

2026-04-27T05:55:01+00:00

A graph $G$ with "p" vertices and "q" edges is called a Polygonal sum graph($PSG$) if it admits a labeling known as Polygonal sum labeling ($PSL$). $PSL$ is an injective function $h:V(G)\rightarrow N$, where $N$ represents the set of all non-negative integers that induces a bijection $h^+:E(G)\rightarrow\{P_K(1),P_K(2),\dots,P_K(q)\}$ of the edges of G defined by $h^{+}(uv)=h(u)+h(v)$ for every $e=uv\in E(G),$ where $P_K(1),P_K(2),\dots,P_K(q)$ are the first "q" polygonal numbers. In this paper we prove that Olive tress, Caterpillars $S(n_1,n_2,\dots,n_m)$ Shrub $St(n_1,n_2,\dots,n_m)$, Banana tree $Bt(n_1,n_2,\dots,n_m)$ and H-graphs are $PSG's$.

Product Order Relatively Prime Graph of a Group

2026-05-14T15:36:30+00:00

In this paper we introduce the concept of a product order relatively prime graph (Simply called PORP graph) $\Gamma_{porp}(G)$ of a finite group $G$. The product order relatively prime graph $\Gamma_{porp}(G)$ is a graph with $V(\Gamma_{porp}(G))=G$ and two vertices $a$ and $b$ are adjacent in $\Gamma_{porp}(G)$ if either $(o(a),o(ab))=1$ or $(o(b),o(ab))=1$. Also we obtain certain graph parameters such as clique number, chromatic number, independent number and domination number.

Mean Labeling of Graphs Associated with Paths and Cycles

2026-05-14T06:11:19+00:00

In mean labeling, unique integer labels are assigned to the vertices such that the each edge receives a distinct label equal to the ceiling of the arithmetic mean of the labels of its incident vertices. In this paper, we prove that the tortoise graph, $PC_n$ graph, $k$-triangular snake graph, and alternate $k$-triangular snake graph admit mean labeling.

Neighborhood Augmented Sombor and Reciprocal Neighborhood Augmented Sombor Indices of Certain Networks

2026-06-13T12:35:13+00:00

In this study, we introduce the neighborhood augmented Sombor and reciprocal neighborhood augmented Sombor indices of a graph. Furthermore, we compute these newly defined neighborhood augmented Sombor indices for certain nanostructures of chemical importance like nanocones and dendrimers.

Fractional Photo-Thermoelastic Semiconductor with Hall Current: A Boundary Value Analysis

2026-05-09T17:11:08+00:00

This study deals with a boundary value problem for a generalized fractional-order photo-thermoelastic semiconductor medium in the presence of Hall current and rotational effects. The formulation is developed within the framework of the Moore-Gibson-Thompson (MGT) heat conduction theory, extended to fractional-order derivatives in time in order to incorporate memory and nonlocal behavior in heat transfer processes. The model accounts for the coupled effects of thermal relaxation, thermal displacement, plasma generation, and electromagnetic interactions, including the Hall current and Lorentz force. The governing equations consist of the fractional-order heat conduction equation, equation of motion, constitutive relations, plasma diffusion equation, and generalized Ohm's law. These equations are formulated as a boundary value problem for a one-dimensional cylindrical semiconductor medium subjected to external laser pulse heating. Appropriate initial and boundary conditions are imposed to ensure the physical relevance of the model. The analytical solution of the problem is obtained using the Laplace transform technique, leading to closed-form expressions in the transform domain. The inversion of the Laplace transform is carried out numerically to obtain the physical distributions of temperature, displacement, carrier density, and stress. Numerical computations are performed for silicon material to examine the influence of key parameters such as fractional order, Hall parameter, rotation, and thermal relaxation time. The results indicate that the fractional-order parameter significantly affects thermal wave propagation and introduces memory-dependent behavior. Moreover, the Hall current and rotational effects are found to have a considerable impact on the thermo-mechanical and electromagnetic responses. The present boundary value formulation provides a comprehensive framework for analyzing coupled thermo-plasma-elastic phenomena in semiconductor materials, with potential applications in modern electronic and photothermal devices.

Slip Velocity and Chemical Reaction Effects on Unsteady Free Convection Flow of MHD Casson Fluid in a Cylinder with Heat and Mass Transfer Through Porous Medium

2026-03-31T06:56:34+00:00

This research paper is focused on a study of the unsteady MHD flow of non-Newtonian Casson fluid with slip velocity and chemical reaction effect in the presence of heat and mass diffusion. The fluid flows past in infinite circular cylinders through a porous medium. The analytic solutions for the velocity profile are derived by using the Laplace transform and the finite Hankel transform. The graphical profiles of velocity are represented to examine and illustrate the impacts of various physical parameters on the significance of physical flow features. The result shows that the slip velocity in the presence of chemical reaction influenced the behaviour of the flow of Casson MHD fluid velocity. Besides that, fluid velocity increases with the increase in the Casson parameter, while it decreases when the magnetic parameter increases. The impact of slip velocity on the flow of fluid decreases at the centre and increases at the boundary of a cylinder. Thus, these findings are beneficial for further exploration in the applications of biomedical engineering and pathology.