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This paper presents the semi-analytical analysis of the fractional-order non-linear coupled system of Whitham-Broer-Kaup equations. An iterative process is designed to analyze analytical findings to the specified non-linear partial fractional derivatives scheme utilizing the Yang transformation coupled with the Adomian technique. The fractional derivative is considered in the sense of Caputo-Fabrizio. Two numerical problems show the suggested method. Moreover, the results of the suggested technique are compared with the solution of other well-known numerical techniques such as the Homotopy perturbation technique, Adomian decomposition technique, and the Variation iteration technique. Numerical simulation has been carried out to verify that the suggested methodologies are accurate and reliable, and the results are revealed using graphs and tables. Comparing the analytical and actual solutions demonstrates that the proposed approaches effectively solve complicated non-linear problems. Furthermore, the proposed methodologies control and manipulate the achieved numerical solutions in a vast acceptable region in an extreme manner. It will provide us with a simple process to control and adjust the convergence region of the series solution.

This work dives into the Conformable Stochastic Kraenkel-Manna-Merle System (CSKMMS), an important mathematical model for exploring phenomena in ferromagnetic materials. A wide spectrum of stochastic soliton solutions that include hyperbolic, trigonometric and rational functions, is generated using a modified version of Extended Direct Algebraic Method (EDAM) namely r +mEDAM. These stochastic soliton solutions have practical relevance for describing magnetic field behaviour in zero-conductivity ferromagnets. By using Maple to generate 2D and 3D graphical representations, the study analyses how stochastic terms and noise impact these soliton solutions. Finally, this study adds to our knowledge of magnetic field behaviour in ferromagnetic materials by shedding light on the effect of noise on soliton processes inside the CSKMMS.

Salt stress is one of the devastating factors that hampers growth and productivity of soybean. Use of Pseudomonas pseudoalcaligenes to improve salt tolerance in soybean has not been thoroughly explored yet. Therefore, we observed the response of hydroponically grown soybean plants, inoculated with halotolerant P. pseudoalcaligenes (SRM-16) and Bacillus subtilis (SRM-3) under salt stress. In vitro testing of 44 bacterial isolates revealed that four isolates showed high salt tolerance. Among them, B. subtilis and P. pseudoalcaligenes showed ACC deaminase activity, siderophore and indole acetic acid (IAA) production and were selected for the current study. We determined that 106 cells/mL of B. subtilis and P. pseudoalcaligenes was sufficient to induce tolerance in soybean against salinity stress (100 mM NaCl) in hydroponics by enhancing plant biomass, relative water content and osmolytes. Upon exposure of salinity stress, P. pseudoalcaligenes inoculated soybean plants showed tolerance by the increased activities of defense related system such as ion transport, antioxidant enzymes, proline and MDA content in shoots and roots. The Na+ concentration in the soybean plants was increased in the salt stress; while, bacterial priming significantly reduced the Na+ concentration in the salt stressed soybean plants. However, the antagonistic results were observed for K+ concentration. Additionally, soybean primed with P. pseudoalcaligenes and exposed to 100 mM NaCl showed a new protein band of 28 kDa suggesting that P. pseudoalcaligenes effectively reduced salt stress. Our results showed that salinity tolerance was more pronounced in P. pseudoalcaligenes as compared to B. subtilis. However, a detailed study at molecular level to interpret the mechanism by which P. pseudoalcaligenes alleviates salt stress in soybean plants need to be explored.

Susceptibility of plants to abiotic stresses, including extreme temperatures, salinity and drought, poses an increasing threat to crop productivity worldwide. Here the drought-induced response of maize was modulated by applications of methyl jasmonate (MeJA) and salicylic acid (SA) to seeds prior to sowing and to leaves prior to stress treatment. Pot experiments were conducted to ascertain the effects of exogenous applications of these hormones on maize growth, physiology and biochemistry under drought stress and well-watered (control) conditions. Maize plants were subjected to single as well as combined pre-treatments of MeJA and SA. Drought stress severely affected maize morphology and reduced relative water content, above and below-ground biomass, rates of photosynthesis, and protein content. The prolonged water deficit also led to increased relative membrane permeability and oxidative stress induced by the production of malondialdehyde (from lipid peroxidation), lipoxygenase activity (LOX) and the production of H2O2. The single applications of MeJA and SA were not found to be effective in maize for drought tolerance while the combined pre-treatments with exogenous MeJA+SA mitigated the adverse effects of drought-induced oxidative stress, as reflected in lower levels of lipid peroxidation, LOX activity and H2O2. The same pre-treatment also maintained adequate water status of the plants under drought stress by increasing osmolytes including proline, total carbohydrate content and total soluble sugars. Furthermore, exogenous applications of MeJA+SA approximately doubled the activities of the antioxidant enzymes catalase, peroxidase and superoxide dismutase. Pre-treatment with MeJA alone gave the highest increase in drought-induced production of endogenous abscisic acid (ABA). Pre-treatment with MeJA+SA partially prevented drought-induced oxidative stress by modulating levels of osmolytes and endogenous ABA, as well as the activities of antioxidant enzymes. Taken together, the results show that seed and foliar pre-treatments with exogenous MeJA and/or SA can have positive effects on the responses of maize seedlings to drought.

Key messageA detailed study of the response of wheat plants, inoculated with drought-tolerant PGPR is studied which would be beneficial to achieve genetic improvement of wheat for drought tolerance.Drought stress, a major challenge under current climatic conditions, adversely affects wheat productivity. In the current study, we observed the response of wheat plants, inoculated with drought-tolerant plant growth-promoting rhizobacteria (PGPR) Bacillus megaterium (MU2) and Bacillus licheniformis (MU8) under induced drought stress. In vitro study of 90 rhizobacteria exhibited 38 isolates showed one or more plant growth-promoting properties, such as solubilization of phosphorus, potassium, and exopolysaccharide production. Four strains revealing the best activities were tested for their drought-tolerance ability by growing them on varying water potentials (− 0.05 to − 0.73 MPa). Among them, two bacterial strains Bacillus megaterium and Bacillus licheniformis showed the best drought-tolerance potential, ACC deaminase activities, IAA production, and antagonistic activities against plant pathogens. Additionally, these strains when exposed to drought stress (− 0.73 MPa) revealed the induction of three new polypeptides (18 kDa, 35 kDa, 30 kDa) in Bacillus megaterium. We determined that 106 cells/mL of Bacillus megaterium and Bacillus licheniformis were enough to induce drought tolerance in wheat under drought stress. These drought-tolerant strains increased the germination index (11–46%), promptness index (16–50%), seedling vigor index (11–151%), fresh weight (35–192%), and dry weight (58–226%) of wheat under irrigated and drought stress. Moreover, these strains efficiently colonized the wheat roots and increased plant biomass, relative water content, photosynthetic pigments, and osmolytes. Upon exposure to drought stress, Bacillus megaterium inoculated wheat plants exhibited improved tolerance by enhancing 59% relative water content, 260, 174 and 70% chlorophyll a, b and carotenoid, 136% protein content, 117% proline content and 57% decline in MDA content. Further, activities of defense-related antioxidant enzymes were also upregulated. Our results revealed that drought tolerance was more evident in Bacillus megaterium as compared to Bacillus licheniformis. These strains could be effective bioenhancer and biofertilizer for wheat cultivation in arid and semi-arid regions. However, a detailed study at the molecular level to deduce the mechanism by which these strains alleviate drought stress in wheat plants needs to be explored.

Nanofluids are extremely beneficial to scientists because of their excellent heat transfer rates, which have numerous medical and industrial applications. The current study deals with the peristaltic flow of nanofluid (i.e., Casson nanofluid) in a symmetric elastic/compliant channel. Buongiorno’s framework of nanofluids was utilized to create the equations for flow and thermal/mass transfer along with the features of Brownian motion and thermophoresis. Slip conditions were applied to the compliant channel walls. The thermal field incorporated the attributes of viscous dissipation, ohmic heating, and thermal radiation. First-order chemical-reaction impacts were inserted in the mass transport. The influences of the Hall current and mixed convection were also presented within the momentum equations. Lubricant approximations were exploited to make the system of equations more simplified for the proposed framework. The solution of a nonlinear system of ODEs was accomplished via a numerical method. The influence of pertinent variables was examined by constructing graphs of fluid velocity, temperature profile, and rate of heat transfer. The concentration field was scrutinized via table. The velocity of the fluid declined with the increment of the Hartman number. The effects of thermal radiation and thermal Grashof number on temperature showed opposite behavior. Heat transfer rate was improved by raising the Casson fluid parameter and the Brownian motion parameter.

This work inspects 3D magnetohydrodynamic hybrid nanofluid flow on a permeable elongating surface. The emphasis of this paper is on the study of hybrid nanofluid flow within a rotating frame, taking into account the simultaneous impact of both thermal and velocity slip boundary conditions. The chosen base fluid is water, and the hybrid nanofluid comprises two nanoparticles and . The effect of the magnetic and porosity parameters is taken into account in the momentum equation. The thermal radiation, Joule heating, and heat source are considered in the energy equation. Using a similarity system, we transform the PDEs of the proposed model into ODEs, which are then solved numerically by the bvp4c technique. The magnetic field shows a dual nature on primary and secondary velocities. Enrich magnetic field decreases the primary velocity and enhances the secondary velocity. The rotation parameter has an inverse relation with both velocities. The temperature profile amplified with the escalation in heat source, magnetic field, rotation factor, and Eckert numbers. The skin friction is boosted with magnetic parameters while the Nusselt number drops.

Fusarium verticillioides is an important fungal pathogen of maize, causing stalk rot and severely affecting crop production. The aim of this study was to characterize the protective effects of formulations based on Jacaranda mimosifolia leaf extracts against F. verticillioides in maize . We compared different seed treatments comprising J. mimosifolia extracts, chemical fungicide (mefenoxam) and salicylic acid to modulate the defense system of maize host plants. Both aqueous and methanolic leaf extracts of J. mimosifolia (1.2% w/v) resulted in 96–97% inhibition of mycelial growth of F. verticillioides . While a full-dose (1.2%) extract of J. mimosifolia provided significant protective effects on maize plants compared to the inoculated control, a half-dose (0.6% w/v) application of J. mimosifolia in combination with half-strength mefenoxam was the most effective treatment in reducing stalk rot disease in pot and field experiments. The same seed treatment significantly upregulated the expression of genes in the leaves encoding chitinase, glucanase, lipid transfer protein, and pathogenesis-related proteins PR-1, PR-5 and PR-10, 72 h after inoculation. This treatment also induced the activities of peroxidase, polyphenol oxidase, protease, acid invertase, chitinase and phenylalanine ammonia lyase. We conclude that seed pre-treatment with J. mimosifolia extract with half-strength chemical mefenoxam is a promising approach for the management of stalk rot in maize.

In this study, a rigorous numerical simulation of the hybrid nanofluid (AA7072-AA7075/methanol) flow over a rotating porous stretching surface is presented. Such a configuration has great importance for aerospace thermal management and high-performance engines' cooling. The main aim is to study the synergistic effect of Soret, Dufour effects, thermal radiation, and exponential heat sources on the efficiency of the fluid flow. For centrifugal pumping systems and heat exchangers that have rotational stresses and multi-physical constraints, such a modeling framework is necessary to optimize the system. This study aims to connect theoretical magnetohydrodynamics with the practical applications to cooling applications within the industrial sector by using the Parametric Continuation Method (PCM). From the comparative analysis of current work, it has been noticed that there is a strong correlation between the current and published results, which ensures the authenticity of these results. From the tabular results, it has been observed that the skin friction enhances up to 74.7319% and 62.0497% by varying the A7072 and AA7075 NPs volume friction from 0.01 to 0.03, whereas it drops up to 34.1635% with the variation in the mixed convection factor. The energy transfer rate enhances up to 22.1359% by varying the thermal radiation factor from 0.3 to 0.7, whereas it drops up to 20.0484% and 21.0407% by varying the exponential heat source parameter and Dufour number from 0.1 to 0.5 and 0.2 to 0.6, respectively. The Sherwood number drops by up to 18.6451% by varying the activation energy factor from 1.0 to 5.0, while enhances up to 17.1852% with variation in the rate of chemical reaction factor.

Drought stress imposes a serious challenge to cultivate wheat, restricting its growth. Drought reduces the capability of plant to uptake essential nutrients. This causes stunted growth, development and yield. Traditional ways to increase wheat growth under drought stress have shortcomings. Using plant-growth-promoting rhizobacteria (PGPR) has proved feasible and eco-friendly way to enhance wheat growth even under the drought stress. Combining PGPR in consortiums further boosts up their effects. In this study, we have checked the efficacy of drought-tolerant Bacillus halotolerans , Pseudomonas sihuiensis and Bacillus atrophaeus in combination. These strains were allowed to grow on PEG 6000 with concentrations (-0.15, -0.49, -0.73 and − 1.2) Mega Pascal (MPa) alone and in combination. Furthermore, Fourier transmission infrared (FTIR) spectroscopy and scanning electron microscopy (SEM) were used. Their biochemical traits such as solubilization of K, P and Zn and the synthesis of siderophore, indole acetic acid (IAA), protease, amylase, hydrogen cyanide (HCN) and 1-aminocyclopropane-1-carboxylate (ACC) deaminase were done. In addition to this, we investigated the optimum folic acid concentration i.e 150 ppm for wheat against drought stress. We conducted a pot experiment to check the growth-enhancing and drought-mitigating effects of consortium and folic acid alone and in combination. As a result, we found a significantly increased wheat biomass, relative water content (RWC), chlorophyll content, antioxidants including glutathione reductase and total soluble sugars and protein content under all treatments. However, the combined treatment of bacterial consortium and folic acid showed maximum potential to boost wheat growth and survival even under drought. We also investigated the minerals uptake by wheat after the treatments and found maximum nutrient uptake under the co-effect of folic acid and bacterial consortium We believe this is the first study that has investigated the optimal dose of folic acid for wheat. Our research is also novel in that we seek to investigate the effects of folic acid along with a bacterial consortium comprising Bacillus halotolerans , Pseudomonas sihuiensis and Bacillus atrophaeus on wheat grown under the drought stress. Highlights Bacillus halotolerans , Pseudomonas sihuiensis and Bacillus atrophaeus are drought tolerant strains. Their consortium significantly improves wheat growth under drought stress. 150 ppm of folic acid is the optimum concentration for wheat growth. Synergistic application of bacterial consortium and folic acid has shown promising wheat growth abilities.