This article applies the homotopy perturbation transform technique to analyze fractional-order nonlinear fifth-order Korteweg–de-Vries-type (KdV-type)/Kawahara-type equations. This method combines the Zain Ul Abadin Zafar-transform (ZZ-T) and the homotopy perturbation technique (HPT) to show the validation and efficiency of this technique to investigate three examples. It is also shown that the fractional and integer-order solutions have closed contact with the exact result. The suggested technique is found to be reliable, efficient, and straightforward to use for many related models of engineering and several branches of science, such as modeling nonlinear waves in different plasma models.

From time immemorial, humans have exploited plants as a source of food and medicines. The World Health Organization (WHO) has recorded 21,000 plants with medicinal value out of 300,000 species available worldwide. The promising modern “multi-omics” platforms and tools have been proven as functional platforms able to endow us with comprehensive knowledge of the proteome, genome, transcriptome, and metabolome of medicinal plant systems so as to reveal the novel connected genetic (gene) pathways, proteins, regulator sequences and secondary metabolite (molecule) biosynthetic pathways of various drug and protein molecules from a variety of plants with therapeutic significance. This review paper endeavors to abridge the contemporary advancements in research areas of multi-omics and the information involved in decoding its prospective relevance to the utilization of plants with medicinal value in the present global scenario. The crosstalk of medicinal plants with genomics, transcriptomics, proteomics, and metabolomics approaches will be discussed.

In this study, some new hypotheses and techniques are presented to obtain some new analytical solutions (localized and periodic solutions) to the generalized Kawahara equation (gKE). As a particular case, some traveling wave solutions to both Kawahara equation (KE) and modified Kawahara equation (mKE) are derived in detail. Periodic and soliton solutions to this family are obtained. The periodic solutions are expressed in terms of Weierstrass elliptic functions (WSEFs) and Jacobian elliptic functions (JEFs). For KE, some direct and indirect approaches are carried out to derive the periodic and localized solutions. For mKE, two different hypotheses in the form of WSEFs are used to derive the periodic and localized solutions. Also, the cnoidal wave solutions in the form of JEFs are obtained. As a realistic physical application, the solutions obtained can be dedicated to studying many nonlinear waves that propagate in plasma.

Motivated by the importance of diffusion equations in many physical situations in general and in plasma physics in particular, therefore, in this study, we try to find some novel solutions to fractional-order diffusion equations to explain many of the ambiguities about the phenomena in plasma physics and many other fields. In this article, we implement two well-known analytical methods for the solution of diffusion equations. We suggest the modified form of homotopy perturbation method and Adomian decomposition methods using Jafari-Yang transform. Furthermore, illustrative examples are introduced to show the accuracy of the proposed methods. It is observed that the proposed method solution has the desire rate of convergence toward the exact solution. The suggested method’s main advantage is less number of calculations. The proposed methods give series form solution which converges quickly towards the exact solution. To show the reliability of the proposed method, we present some graphical representations of the exact and analytical results, which are in strong agreement with each other. The results we showed through graphs and tables for different fractional-order confirm that the results converge towards exact solution as the fractional-order tends towards integer-order. Moreover, it can solve physical problems having fractional order in different areas of applied sciences. Also, the proposed method helps many plasma physicists in modeling several nonlinear structures such as solitons, shocks, and rogue waves in different plasma systems.

To satisfy the electricity needs of a village in Tangi, northwest Pakistan, the present research can design and evaluate the environmental and economical aspects of an optimal hybrid photovoltaic-biogas-hydropower-battery energy sustainable system (PV-BG-HP-BESS). This framework integrates various renewable energy sources, delivering a modern, efficient approach to sustainable energy solutions. The HOMER Pro software is utilized to optimize the most economical and effective hybrid energy system. The results showed that the proposed hybrid system comprising 91.4 kWp PV modules, 19.6 kW hydropower, a 50 kW biogas generator (BG), 36 batteries, and a 60.6 kW converter was the most economical choice. This system, which used the cyclic charging (CC) method, had a cost of energy (COE) of 0.0728 $/kWh and a total net present cost (NPC) of $152,242. The suggested hybrid energy system for rural areas of Pakistan includes photovoltaic (PV), biogas (BG), hydro, and battery components to provide a dependable and sustainable power supply. This system minimizes the need for expensive fossil fuels while simultaneously minimizing environmental impact by lowering pollutants and greenhouse gas emissions. The system's annual electricity production is 294,782 kWh, with PV leads at 59.4%, BG at 6.02%, and hydro at 34.6%, ensuring uninterrupted power generation even in remote areas. The unmet load, extra electricity, and capacity shortage illustrate the reliability of the system and make it possible to address rural electrification challenges while supporting sustainable development and economic growth. Moreover, the outcomes of the proposed hybrid system dominate the previous studies in multiple objectives, including cost and sensitivity analysis, when compared.