Boletim da Sociedade Paranaense de Matemática

Ms. Numerical Approach for Solving Fredholm Integro-Fractional Differential Equations with Numerous Constant Delays Based on Newton-Cotes Methods

2026-04-30T10:40:59+00:00

This article presents strong algorithms for the numerical solution of linear Fredholm integrofractional
differential equations of constant delay type (FIFDEs-Delays) with variable coefficients under boundary
conditions with historical functions and the fractional order less than or equal to one in the Caputo sense.
With the aid of a finite difference approximation for Caputo derivative utilization collocation points, the approach
is based on the Newton-Cotes methods. Our method transforms the original FIFDEs-Dealays equation
into a set of algebraic equations with operational matrices for treatments, which are then numerically solved.
This approach covers the integral component of the equation by utilizing the power of Newton-Cotes quadrature
rules, such as the trapezoidal or Simpson’s 1/3 rules, which makes evaluation easy.Furthermore, a number
of numerical examples are provided to assess the effectiveness of proposed approach, proving its accuracy and
practicality. General programs are written in Python.

The Bi-Fox-Wright Function Srivastava Triple Hypergeometric Function (_^Ψ)H_(A;p,q)^(m,n) (.) and Applications of the Multiple Laplace Transform

2026-04-30T10:43:51+00:00

The aim of this work is to introduce bi-Fox-Wright Function Srivastava triple hypergeometric function that includes two Fox-Wright functions as its kernel, demonstrating how it simplifies to certain established results in the literature. The discussion includes properties such as integral representations, differential formulas, and recurrence relations. Additionally, connections between the double Mellin transform and the Laplace transform are established.

Applications of Fuzzy Maximal $\mu$-open sets in Generalized Fuzzy Topology and Fuzzy Quasi Topology

2026-04-30T13:06:55+00:00

This work explores key characteristics of fuzzy maximal $\mu$-open sets in the setting of a generalized fuzzy topological space. A decomposition theorem for fuzzy maximal $\mu$-open sets is presented, along with fundamental results regarding their intersections. In addition, a formulation consistent with the fuzzy $\mu$-radical $\mu$-closure is established in the framework of quasi-fuzzy topological spaces other related findings.

Ideal-Based Wijsman Convergence in Intuitionistic Fuzzy 2-Metric Frameworks

2026-04-30T13:10:16+00:00

Motivated by \cite{MDM09}'s notion of intuitionistic fuzzy 2-metric space (briefly, IF-2MS), we conduct a thorough investigation and analysis of Wijsman

ideal convergence within an IF-2MS.This exploration provides a novel framework for assessing the convergence behavior of set sequences in 2-metric spaces. Additionally, we elucidate the relationship between Wijsman ideal Cauchy sequences

and Wijsman ideal convergence within this innovative framework. Furthermore, we analyze $\mathcal{J}-$ limit points and $\mathcal{J}-$ cluster ponits, and establish the inclusion relationship between them in this context.

Convergence of mutivalued martingale : Application to multivalued uniform amarts

2026-04-30T13:13:47+00:00

In this work, we prove a convergence theorem for bounded martingales taking values in a Banach space Y, without requiring Y to have the Radon Nikodym Property. We then extend this result to martingales with values in ccb(Y) (the set of nonempty, convex, closed, and bounded subsets of Y )under several topologies. As applications, we show the convergence of multivalued uniform asymptotic martingales with values in ccb(Y).

An application to explore the progress of a nation using the emerging nano topological concepts via multiple ideals

2026-04-30T13:19:48+00:00

The idea of nano topology was constituted by M.L. Thivagar wherein topology was generated using an intriguing methodology of approximation of rough sets. As the approach of approximation using the multiple ideals gives a higher value of accuracy when compared to the existing notions, the objective of this paper is to propose the nearly open forms of j-multi ideal nano topology, such as j-multi ideal nano semi-open, j-multi ideal nano pre-open, j-multi ideal nano regular open and j-multi ideal nano $\alpha$ open sets. An interrelation of all these open forms is illustrated. Various nano continuities using multi-ideal approximation technique are introduced and their interconnection is studied. Some nano separation axioms using this ideology are defined. A real-life example of nano topology is also discussed towards the end of this paper to find the key factors that govern the development or underdevelopment of a nation.

Impacts of Magneto-hydrodynamics and slip velocity effects on curved circular and Porous- Rough flat plate lubricated with couple stress Fluid.

2026-04-30T13:28:22+00:00

This work investigates, using a couple stress fluids, the combined impacts of MHD and slip velocity on the lubrication performance of curved-circular flat surfaces with the effect of porous-rough bearing. Derived and investigated under several operating situations are expressions for MHD squeeze film pressure, load capacity, and squeeze film time. Results imply that an external magnetic field helps the squeeze film properties to become better in an electrically conducting non-Newtonian fluid. Whereas radial roughness lowers these features relative to smooth surfaces, azimuthal surface roughness enhances them. Emphasizing the limits of porous materials, the permeability parameter negatively affects pressure, load capacity, and squeeze-film time. These results progress understanding of lubrication performance under MHD impacts in complex systems.

Characterizations of $e^\star$-open sets and nearby open sets on Infra topological spaces

2026-04-30T13:35:41+00:00

The study of infra-topological spaces focuses on characterizations of $e^\star$-open sets and nearby open sets in infra-topological spaces. The $e^\star$-open sets, a variation of open sets, are explored for their unique properties and relationships within the infra-topological framework. Additionally, nearby open sets, which capture the notion of points being close to each other, are investigated to provide a comprehensive understanding of the topological structure. The research aims to contribute to the broader field of topology by extending traditional concepts to infra-topological spaces, offering new perspectives on openness and proximity. The findings not only deepen our understanding of mathematical structures but also open avenues for applications in various scientific and engineering disciplines.