The purpose of this paper is to determine the existence of tripled fixed point results for the tripled symmetry system of fractional hybrid delay differential equations. We obtain results which support the existence of at least one solution to our system by applying hybrid fixed point theory. Similar types of stability analysis are presented, including Ulam–Hyers, generalized Ulam–Hyers, Ulam–Hyers–Rassias, and generalized Ulam–Hyers–Rassias. The necessary stipulations for obtaining the solution to our proposed problem are established. Finally, we provide a non-trivial illustrative example to support and enhance our analysis.

The purpose of this manuscript is to demonstrate the existence and uniqueness of triple fixed-point results for Geraghty-type contractions in ordinary metric spaces with binary relations. Moreover, the well-posedness of the tripled fixed point problem is investigated. Consequently, $\alpha$-dominated mapping on such space is discussed. Ultimately, to promote our paper, some illustrative examples are derived, and the existence of the solution to a system of differential equations is obtained as an application.

The main objective of this paper is to investigate the deformation behavior in a two-dimensional homogeneous, isotropic thermo-elastic half-space subjected to an external heat source applied at its boundary and electro-magnetic field, within the framework of the Lord-Shulman theory. The novelty of this work lies in formulating a new coupled dynamic model that integrates mechanical stresses with temperature interactions in an elastic medium. The Lame’s potential method and normal mode analysis method is applied to solve the resulting coupled differential equations, obtaining both deterministic and solutions. The temperature, displacement component and stress components of these waves are obtained analytically with the use of suitable boundary conditions. Focusing on aluminium epoxy-like material, graphical representations of numerically simulated findings using MATHEMATICA software show how time, magnetic field and permeability of electric field. The work includes detailed graphical representations of crucial discoveries such as temperature distributions, stress components, and displacement components which provide amazing visual insights into the complex interactions that occur within thermo-elastic systems. From the distributions, it can be found the wave type heat propagation in the medium. A comparison is made with the results obtained in the presence and absence of the electro-magnetic field. By forging a link between theoretical insights and practical applications, this study stands to make a significant contribution to the field of materials science, providing a solid foundation for subsequent inquiries within this rapidly progressing arena. A graphic comparison of our physical quantity accuracy results with earlier studies shows the significant influence of electro-magnetic field on thermoelastic phenomena. The analysis of thermoelastic problems with electro-magnetic field benefits from the study.

This manuscript is devoted to obtaining tripled fixed point results in the setting of orthogonal metric spaces. Also, some corollaries are presented. Furthermore, we obtained some results of the existence and uniqueness for tripled fixed point for orthogonal complete metric spaces which are not satisfied for complete metric spaces and we discussed this in an example. Ultimately, to support the theoretical results, a system of nonlinear integral equations is given as an application.