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Fractional order nonlinear evolution equations (FNLEEs) pertaining to conformable fractional derivative are considered to be revealed for well-furnished analytic solutions due to their importance in the nature of real world. In this article, the autors suggest a productive technique, called the rational fractional (DξαG/G)-expansion method, to unravel the nonlinear space-time fractional potential Kadomtsev–Petviashvili (PKP) equation, the nonlinear space-time fractional Sharma–Tasso–Olver (STO) equation and the nonlinear space-time fractional Kolmogorov–Petrovskii–Piskunov (KPP) equation. A fractional complex transformation technique is used to convert the considered equations into the fractional order ordinary differential equation. Then the method is employed to make available their solutions. The constructed solutions in terms of trigonometric function, hyperbolic function and rational function are claimed to be fresh and further general in closed form. These solutions might play important roles to depict the complex physical phenomena arise in physics, mathematical physics and engineering.

The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is of the form U(ξ)=∑i=0nai(DξαG/G)i/∑i=0nbi(DξαG/G)i.

Achieved fresh and further abundant closed form traveling wave solutions to analyze the inner mechanisms of complex phenomenon in nature world which will bear a significant role in the of research and will be recorded in the literature.

The rational fractional (DξαG/G)-expansion method shows high performance and might be used as a strong tool to unravel any other FNLEEs. This method is newly established and productive.

Sustainable manufacturing is one of the most important and most challenging issues in present industrial scenario. With the intention of diminish negative effects associated with cutting fluids, the machining industries are continuously developing technologies and systems for cooling/lubricating of the cutting zone while maintaining machining efficiency. In the present study, three regression based machine learning techniques, namely, polynomial regression (PR), support vector regression (SVR) and Gaussian process regression (GPR) were developed to predict machining force, cutting power and cutting pressure in the turning of AISI 1045. In the development of predictive models, machining parameters of cutting speed, depth of cut and feed rate were considered as control factors. Since cooling/lubricating techniques significantly affects the machining performance, prediction model development of quality characteristics was performed under minimum quantity lubrication (MQL) and high-pressure coolant (HPC) cutting conditions. The prediction accuracy of developed models was evaluated by statistical error analyzing methods. Results of regressions based machine learning techniques were also compared with probably one of the most frequently used machine learning method, namely artificial neural networks (ANN). Finally, a metaheuristic approach based on a neural network algorithm was utilized to perform an efficient multi-objective optimization of process parameters for both cutting environment.

In this study, the authors propose a novel digital twinning approach specifically designed for controlling transient thermal systems. The purpose of this study is to harness the combined power of deep learning (DL) and physics-based methods (PBM) to create an active virtual replica of the physical system.

To achieve this goal, we introduce a deep neural network (DNN) as the digital twin and a Finite Element (FE) model as the physical system. This integrated approach is used to address the challenges of controlling an unsteady heat transfer problem with an integrated feedback loop.

The results of our study demonstrate the effectiveness of the proposed digital twinning approach in regulating the maximum temperature within the system under varying and unsteady heat flux conditions. The DNN, trained on stationary data, plays a crucial role in determining the heat transfer coefficients necessary to maintain temperatures below a defined threshold value, such as the material’s melting point. The system is successfully controlled in 1D, 2D and 3D case studies. However, careful evaluations should be conducted if such a training approach, based on steady-state data, is applied to completely different transient heat transfer problems.

The present work represents one of the first examples of a comprehensive digital twinning approach to transient thermal systems, driven by data. One of the noteworthy features of this approach is its robustness. Adopting a training based on dimensionless data, the approach can seamlessly accommodate changes in thermal capacity and thermal conductivity without the need for retraining.

This study aims to investigate the suitability of a multi-step prototyping strategy for producing pneumatic rotary vane actuators (RVAs) for the development of lightweight robots and actuation systems.

RVAs typically have cast aluminum housings and injection-molded seals that consist of hard thermoplastic cores and soft elastomeric overmolds. Using a combination of additive manufacturing (AM), computer numerical control (CNC) machining and elastomer molding, a conventionally manufactured standard RVA was replicated. The standard housing design was modified, and polymeric replicas were obtained by selective laser sintering (SLS) or PolyJet (PJ) printing and subsequent CNC milling. Using laser-sintered molds, actuator seals were replicated by overmolding laser-sintered polyamide cores with silicone (SIL) and polyurethane (PU) elastomers. The replica RVAs were subjected to a series of leakage, friction and durability experiments.

The AM-based prototyping strategy described is suitable for producing functional and reliable RVAs for research and product development. In a representative durability experiment, the RVAs in this study endured between 40,000 and 1,000,000 load cycles. Frictional torques were around 0.5 Nm, which is 10% of the theoretical torque at 6 bar and comparable to that of the standard RVA. Models and parameters are provided for describing the velocity-dependent frictional torque. Leakage experiments at 10,000 load cycles and 6 bar differential pressure showed that PJ housings exhibit lower leakage values (6.8 L/min) than laser-sintered housings (15.2 L/min), and PU seals exhibit lower values (8.0 l/min) than SIL seals (14.0 L/min). Combining PU seals with PJ housings led to an initial leakage of 0.4 L/min, which increased to only 1.2 L/min after 10,000 load cycles. Overall, the PU material used was more difficult to process but also more abrasion- and tear-resistant than the SIL elastomer.

More work is needed to understand individual cause–effect relationships between specific design features and system behavior.

To date, pneumatic RVAs have been manufactured by large-scale production technologies. The absence of suitable prototyping strategies has limited the available range to fixed sizes and has thus complicated the use of RVAs in research and product development. This paper proves that functional pneumatic RVAs can be produced by using more accessible manufacturing technologies and provides the tools for prototyping of application-specific RVAs.

This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and uniqueness are proved. The authors divide the proof into two sections for the linear associated problem; the authors derive the a priori bound and demonstrate the operator range density that is generated. The authors solve the nonlinear problem by introducing an iterative process depending on the preceding results.

The functional analysis method is the a priori estimate method or energy inequality method.

The results show the efficiency of a priori estimate method in the case of time-fractional order differential equations with nonlocal conditions. Our results also illustrate the existence and uniqueness of the continuous dependence of solutions on fractional order differential equations with nonlocal conditions.

The authors’ work can be considered a contribution to the development of the functional analysis method that is used to prove well-positioned problems with fractional order.

The authors confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.