This study addresses a nonlinear fractional Drinfeld–Sokolov–Wilson problem in dispersive water waves, which requires appropriate numerical techniques to obtain an approximative solution. The Adomian decomposition approach, the homotopy perturbation method, and Sumudu transform are combined to tackle the problem. The Caputo manner is used to describe fractional derivative, and He’s polynomials and Adomian polynomials are employed to address nonlinearity. By following these approaches, we obtain solutions in the form of convergent series. We verify and demonstrate the effectiveness of our suggested strategies by examining the assumed model in terms of fractional order. We use plots for various fractional orders to represent the physical behavior of the suggested technique solutions, and show a numerical simulation. The results demonstrate that the suggested algorithms are systematic, simple to use, effective, and accurate in analyzing the behavior of coupled nonlinear differential equations of fractional order in related scientific and engineering fields.

Fuel cells guarantee ecological ways of electricity production by promising zero emissions. Proton exchange membrane fuel cells (PEMFCs) are considered one of the safest methods, with a low operating temperature and maximum conversion efficiency. In order to harness the full potential of PEMFC, it is imperative to ensure the membrane’s safety through appropriate control strategies. However, most of the strategies focus on fuel economy along with viable fuel cell life, but they do not assure constant output voltage characteristics. A comprehensive design to regulate and boost the output voltages of PEMFC under varying load conditions is addressed with dynamic integral sliding mode control (DISMC) by combining the properties of both the dynamic and integral SMC. The proposed system outperforms in robustness against parametric uncertainties and eliminates the reaching phase along with assured stability. A hardware test rig consisting of a portable PEMFC is connected to the power converter using the proposed technique that regulates voltage for varying loads and power conditions. The results are compared with a proportional integral (PI) based system. Both simulation and hardware results are provided to validate the proposed technique. The experimental results show improvements of $35.4\%$, $34\%$ and $50\%$ in the rise time, settling time and robustness, respectively.

The p53 pathway has been the focus of many researchers in the last few decades owing to its pivotal role as a frontline cancer suppressant protein. It plays a vital role in maintaining cell cycle checkpoints and cell apoptosis in response to a broken DNA strand. This is why it is found in the mutated form in more than 50% of malignant tumors. To overcome this, various drugs have been proposed to revive the p53 pathway in cancer patients. Small-molecule-based drugs, such as Nutlin 3a, which are capable of performing this stimulation, are at the fore of advanced clinical trials. However, the calculation of their dosage is a challenge. In this work, a method to determine the dosage of Nutlin 3a is investigated. A control-systems-based model is developed to study the response of the wild-type p53 protein to this drug. The proposed strategy regulates the p53 protein along with negative and positive feedback loops mediated by the MDM2 and MDM2 mRNA, respectively, along with the reversible repression of MDM2 caused by Nutlin 3a. For a broader perspective, the reported PBK dynamics of Nutlin 3a are also incorporated. It has been reported that p53 responds to stresses in two ways in terms of concentration to this drug: either it is a sustained (constant) or an oscillatory response. The claimed dosage strategy turned out to be appropriate for sustained p53 response. However, for the induction of oscillations, inhibition of MDM2 is not enough; rather, anti-repression of the p53–MDM2 complex is also needed, which opens new horizons for a new drug design paradigm.