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This study aims to present the notions of interpolative Prešić-type set-valued contractions for the set-valued operators defined on product spaces. With the help of these notions, we have studied the existence of fixed points for such set-valued operators. An application of the obtained results is also discussed with the help of graph theory.

In this article, we have designed two existence of fixed point theorems which are regarding to set-valued SU-type θ η -contraction and Γ α -contraction via gauge function in the setting of metric spaces. An extensive set of nontrivial example will be given to justify our claim. At the end, we will give an application to prove the existence behavior for the system of functional equation in dynamical system and integral inclusion.

This study presents numerical work to investigate the Falkner–Skan flow of a bio-convective Casson fluid over a wedge using an Evolutionary Padé Approximation (EPA) scheme. The governing partial differential equations and boundary conditions of a Falkner–Skan flow model are transformed to a system of ordinary differential equations involving ten dimensionless parameters by using similarity transformations. In the proposed EPA framework, an equivalent constrained optimization problem is formed. The solution of the resulting optimization problem is analogous to the solution of the dimensionless system of ordinary differential equations. The solutions produced in this work, with respect to various combinations of the physical parameters, are found to be in good agreement with those reported in the previously published literature. The effects of a non-dimensional physical-parameter wedge, Casson fluid, fluid phase effective heat capacity, Brownian motion, thermophoresis, radiation, and magnetic field on velocity profile, temperature profile, fluid concentration profile, and the density of motile microorganisms are discussed and presented graphically. It is observed that the fluid velocity rises with a rise in the Casson fluid viscosity force parameter, and an increase in the Prandtl number causes a decrease in the heat transfer rate. Another significant observation is that the temperature and fluid concentration fields are greatly increased by an increase in the thermophoresis parameter. An increase in the Péclet number suppresses the microorganism density. Moreover, the increased values of the Prandtl number increase the local Nusslet number, whereas the skin friction is increased when an increase in the Prandtl number occurs.