In this article, free convection flow of an Oldroyd-B fluid (OBF) through a vertical rectangular channel in the presence of heat generation or absorption subject to generalized boundary conditions is studied. The fractionalized mathematical model is established by Caputo time-fractional derivative through mechanical laws (generalized shear stress constitutive equation and generalized Fourier’s law). Closed form solutions for the velocity and temperature profiles are obtained via Laplace coupled with sine-Fourier transforms and have been embedded with regards to the special functions, namely, the generalized G-functions of Lorenzo and Hartley. Solutions of the known results from recently published work (Nehad et al. Chin. J. Phy., 65, (2020) 367–376) are recovered as limiting cases. Finally, the effects of fractional and various physical parameters are graphically underlined. Furthermore, a comparison between Oldroyd-B, Maxwell and viscous fluids (fractional and ordinary) is depicted. It is found that, for short time, ordinary fluids have greater velocity as compared to the fractional fluids.

This article presents the problem, in which we study the unsteady double convection flow of a magnetohydrodynamics (MHD) differential-type fluid flow in the presence of heat source, Newtonian heating, and Dufour effect over an infinite vertical plate with fractional mass diffusion and thermal transports. The constitutive equations for the mass flux and thermal flux are modeled for noninteger-order derivative Caputo–Fabrizio (CF) with nonsingular kernel, respectively. The Laplace transform and Laplace inversion numerical algorithms are used to derive the analytical and semianalytical solutions for the dimensionless concentration, temperature, and velocity fields. Expressions for the skin friction and rates of heat and mass transfer from the plate to fluid with noninteger and integer orders, respectively, are also determined. Furthermore, the influence of flow parameters and fractional parameters α and β on the concentration, temperature, and velocity fields are tabularly and graphically underlined and discussed. Furthermore, a comparison between second-grade and viscous fluids for noninteger and integer is also depicted. It is observed that integer-order fluids have greater velocities than noninteger-order fluids. This shows how the fractional parameters affect the fluid flow.

<abstract><p>Optimization techniques can be used to find the optimal combination of inputs and parameters and help identify the most efficient solution. Aggregation operators (AOs) play a prominent role in discernment between two circulations of prospect and pull out anxieties from that insight. The most fundamental objective of this research is to extend the interaction AOs to the interval-valued Pythagorean fuzzy hypersoft set (IVPFHSS), the comprehensive system of the interval-valued Pythagorean fuzzy soft set (IVPFSS). The IVPFHSS adroitly contracts with defective and ambagious facts compared to the prevalent Pythagorean fuzzy soft set and interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS). It is the dominant technique for enlarging imprecise information in decision-making (DM). The most important intention of this exploration is to intend interactional operational laws for IVPFHSNs. We extend the AOs to interaction AOs under IVPFHSS setting such as interval-valued Pythagorean fuzzy hypersoft interactive weighted average (IVPFHSIWA) and interval-valued Pythagorean fuzzy hypersoft interactive weighted geometric (IVPFHSIWG) operators. Also, we study the significant properties of the proposed operators, such as Idempotency, Boundedness, and Homogeneity. Still, the prevalent multi-criteria group decision-making (MCGDM) approaches consistently carry irreconcilable consequences. Meanwhile, our proposed MCGDM model is deliberate to accommodate these shortcomings. By utilizing a developed mathematical model and optimization technique, Industry 5.0 can achieve digital green innovation, enabling the development of sustainable processes that significantly decrease environmental impact. The impacts show that the intentional model is more operative and consistent in conducting inaccurate data based on IVPFHSS.</p></abstract>

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