This article includes some fixed point results for (φ,ψ,θ)-contractions in the context of metric space endowed with a locally H-transitive relation. We constructed an example for attesting to the credibility of our results. We also discussed the existence and uniqueness of the solution of a Fredholm integral equation using our results.

After the appearance of relation-theoretic contraction principle due to Alam and Imdad, the domain of fixed point theory applied to relational metric spaces has attracted much attention. Existence and uniqueness of fixed/coincidence points satisfying the different types of contractivity conditions in the framework of relational metric space have been studied in recent times. Such results have the great advantage to solve certain types of matrix equations and boundary value problems for ordinary differential equations, integral equations and fractional differential equations. This article is devoted to proving the coincidence and common fixed point theorems for a pair of mappings (T,S) employing relation-theoretic (ϕ,ψ)-contractions in a metric space equipped with a locally finitely T-transitive relation. Our results improve, modify, enrich and unify several existing coincidence points as well as fixed point results. Several examples are provided to substantiate the utility of our results.

This article discusses a variety of important notions, including ideal convergence and ideal Cauchyness of topological sequences produced by fuzzy normed spaces. Furthermore, the connections between the concepts of the ideal limit and ideal cluster points of a sequence in a fuzzy normed linear space are investigated. In a fuzzy normed space, we investigated additional effects, such as describing compactness in terms of ideal cluster points and other relevant but previously unresearched ideal convergence and adjoint ideal convergence aspects of sequences and nets. The countable compactness of a fuzzy normed space and its link to it were also defined. The terms ideal and its adjoint divergent sequences are then introduced, and specific aspects of them are explored in a fuzzy normed space. Our study supports the importance of condition (AP) in examining summability via ideals. It is suggested to use a fuzzy point symmetry-based genetic clustering method to automatically count the number of clusters in a data set and determine how well the data are fuzzy partitioned. As long as the clusters have the attribute of symmetry, they can be any size, form, or convexity. One of the crucial ways that symmetry is used in fuzzy systems is in the solution of the linear Fuzzy Fredholm Integral Equation (FFIE), which has symmetric triangular (Fuzzy Interval) output and any fuzzy function input.

The present study deals with electrically conductive fluid flow across a heated circular cylinder to examine the oscillatory magnetic flux and heat transfer in the presence of variable surface temperature. The proposed mathematical formulation is time-dependent, which is the source of the amplitude and fluctuation in this analysis. The designed fluctuating nonlinear computational model is associated with the differential equations under specific boundary conditions. The governing equations are converted into dimensionless form by using adequate dimensionless variables. To simplify the resolution of the set of governing equations, it is further reduced. The effects of surface temperature parameter β, magnetic force number ξ, buoyancy parameter λ, Prandtl number Pr, and magnetic Prandtl parameter γ are investigated. The main finding of the current study is related to the determination of the temperature distribution for each inclination angle. It is seen that a higher amplitude of the heat transfer rate occurs as the surface temperature increases. It is also noticed that the oscillatory magnetic flux becomes more important as the magnetic Prandtl number increases at each position. The present magneto-thermal analysis is significantly important in practical applications such as power plants, thermally insulated engines, and nuclear reactor cooling.

Scientists and researchers are much interested in studying graphene and silver nanoparticles for the enhancement of heat transport due to their extensive variety of applications in different areas of industrial and engineering such as drug delivery, medical devices, ultra-light, excellent electrical conductivity, strong medical strength, health care, consumer, food, etc. Therefore, in the existing investigation, the MHD flow of a mixed convective hybrid nanoliquid with graphene and silver nanoparticles past a rotating disk is considered. Water and ethylene glycol (50:50) is used as a base liquid in the existing model. The mechanism for heat transport is computed with the existence of thermal radiation and thermal convective condition. Homogeneous and heterogeneous chemical reactions are assumed in the flow behavior. The mathematical formulation of the proposed problem is based on the nonlinear PDEs which are then transformed to nonlinear ODEs by manipulating the appropriate similarity transformation. The simulation of the existing problem has been performed with the help of the homotopy analysis technique. The outcomes of the different flow parameters on the velocities, temperature, concentration, skin friction coefficient, and Nusselt number of the hybrid nanofluid are attained via graphs and tables. Some significant results from the existing problem demonstrate that the rate of heat transport is greater for the thermal Biot number and nanoparticles volume fraction. Further, it is noticed that the velocity of the liquid particles becomes lower for a higher magnetic field parameter.