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In this paper, we investigate the generalized Langevin-Sturm-Liouville differential problems involving Caputo-Atangana-Baleanu fractional derivatives of higher orders with respect to another positive, increasing function denoted by ρ. The fixed point theorems in the framework of Kransnoselskii and Banach are utilized to discuss the existence and uniqueness of the results. In addition, the stability criteria of Ulam-Hyers, generalize Ulam-Hyers, Ulam-Hyers-Rassias, and generalize Ulam-Hyers-Rassias are investigated by non-linear analysis besides fractional calculus. Finally, illustrative examples are reinforced by tables and graphics to describe the main achievements., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Thabet et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

The internal atmospheric waves are gravity waves and occur in the inner part of the fluid system. In this study, a time-fractional model for internal atmospheric waves is investigated with the Caputo-Fabrizio time-fractional differential operator. The analytical solution of the considered model is retrieved by the Elzaki Adomian decomposition method. The variation in the solution is examined for increasing order of the fractional parameter α through numerical and graphical simulations. The accuracy of the obtained results is established by comparing the obtained solution of considered fractional model with the results available in the literature., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Vivas-Cortez et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

This research manuscript aims to study a novel implicit differential equation in the non-singular fractional derivatives sense, namely Atangana-Baleanu-Caputo ([Formula: see text]) of arbitrary orders belonging to the interval (2, 3] with respect to another positive and increasing function. The major results of the existence and uniqueness are investigated by utilizing the Banach and topology degree theorems. The stability of the Ulam-Hyers ([Formula: see text]) type is analyzed by employing the topics of nonlinear analysis. Finally, two examples are constructed and enhanced with some special cases as well as illustrative graphics for checking the influence of major outcomes., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Rezapour et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

This research work is devoted to investigating new common fixed point theorems on bipolar fuzzy [Formula: see text]-metric space. Our main findings generalize some of the existence outcomes in the literature. Furthermore, we illustrate our findings by providing some applications for fractional differential and integral equations., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Maheswari et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

To analyze and study the behaviour of the shallow water waves, the perturbed Boussinesq equation has acquired fundamental importance. The principal objective of this paper is to manifest the exact traveling wave solution of the perturbed Boussinesq equation by two well known techniques named as, two variables [Formula: see text] expansion method and generalized projective Riccati equations method. A diverse array of soliton solutions, encompassing periodic, bright solitons, singular solitons and bright singular solitons are obtained by the applications of proposed techniques. The constraint conditions for newly constructed solutions are also specified. To enhance comprehension, the numerical illustrations of constructed solutions have been represented using surface plots, 2D plots and density plots. The results delineated in this paper transcend existing analysis, offering a novel, well-structured, and modern perspective. The solutions obtained not only enrich understanding of shallow water wave models but also exhibit efficacy in providing detailed descriptions of their dynamics., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Vivas-Cortez et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

This article delves into examining exact soliton solutions within the context of the generalized nonlinear Schrödinger equation. It covers higher-order dispersion with higher order nonlinearity and a parameter associated with weak nonlocality. To tackle this equation, two reputable methods are harnessed: the sine-Gordon expansion method and the [Formula: see text]-expansion method. These methods are employed alongside suitable traveling wave transformation to yield novel, efficient single-wave soliton solutions for the governing model. To deepen our grasp of the equation's physical significance, we utilize Wolfram Mathematica 12, a computational tool, to produce both 3D and 2D visual depictions. These graphical representations shed light on diverse facets of the equation's dynamics, offering invaluable insights. Through the manipulation of parameter values, we achieve an array of solutions, encompassing kink-type, dark soliton, and solitary wave solutions. Our computational analysis affirms the effectiveness and versatility of our methods in tackling a wide spectrum of nonlinear challenges within the domains of mathematical science and engineering., Competing Interests: NO authors have competing interests., (Copyright: © 2024 Vivas-Cortez et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

This research paper focuses on the study of the (3+1)-dimensional negative order KdV-Calogero-Bogoyavlenskii-Schiff (KdV-CBS) equation, an important nonlinear partial differential equation in oceanography. The primary objective is to explore various solution techniques and analyze their graphical representations. Initially, two wave, three wave, and multi-wave solutions of the negative order KdV CBS equation are derived using its bilinear form. This analysis shed light on the behavior and characteristics of the equation's wave solutions. Furthermore, a bilinear Bäcklund transform is employed by utilizing the Hirota bilinear form. This transformation yields exponential and rational function solutions, contributing to a more comprehensive understanding of the equation. The resulting solutions are accompanied by graphical representations, providing visual insights into their structures. Moreover, the extended transformed rational function method is applied to obtain complexiton solutions. This approach, executed through the bilinear form, facilitated the discovery of additional solutions with intriguing properties. The graphical representations, spanning 2D, 3D, and contour plots, serve as valuable visual aids for understanding the complex dynamics and behaviors exhibited by the equation's solutions., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2024 Vivas-Cortez et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

This article deals with studying the dynamical behavior of the DNA model proposed by Peyrard and Bishop. The proposed model is investigated using the unified method (UM). Unified method successfully extracts solutions in the form of polynomial and rational functions. The solitary wave solutions and soliton solutions are constructed. An investigation of modulation instability is also presented in this paper. 3D and 2D plots are presented to exhibit the physical behavior of some of the obtained solutions., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Vivas-Cortez et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

The identification of the genes responsible for complex traits is highly promising to accelerate crop breeding, but such information is still limited for popcorn. Thus, in the present study, a mixed linear model-based association analysis (MLMA) was applied for six important popcorn traits: plant and ear height, 100-grain weight, popping expansion, grain yield and expanded popcorn volume per hectare. To this end, 196 plants of the open-pollinated popcorn population UENF-14 were sampled, selfed (S1), and then genotyped with a panel of 10,507 single nucleotide polymorphisms (SNPs) markers distributed throughout the genome. The six traits were studied under two environments [Campos dos Goytacazes-RJ (ENV1) and Itaocara-RJ (ENV2)] in an incomplete block design. Based on the phenotypic data of the S1 progenies and on the genetic characteristics of the parents, the MLMA was performed. Thereafter, genes annotated in the MaizeGDB platform were screened for potential linkage disequilibrium with the SNPs associated to the six evaluated traits. Overall, seven and eight genes were identified as associated with the traits in ENV1 and ENV2, respectively, and proteins encoded by these genes were evaluated for their function. The results obtained here contribute to increase knowledge on the genetic architecture of the six evaluated traits and might be used for marker-assisted selection in breeding programs., Competing Interests: The author JEdAF is affiliated to commercial company Bayer, the author GFP is affiliated to Universidade Estadual de Mato Grosso, and the authors CM and FM are affiliated to Universidad de Talca. This does not alter our adherence to PLOS ONE policies on sharing data and materials.

Agricultural expansion and the need for sustainable cultivation are challenges faced by researchers involved in the generation of new cultivars that can adapt to abiotic stress. Knowledge of the genetic effects of characteristics related to efficiency and responsiveness to phosphorus use must be considered when implementing methods to obtain better genotypes. The aim of this study was to characterize and select popcorn hybrids based on their efficiency and responsiveness to phosphorus use, and estimate their combining abilities and genetic effects via diallel analysis to implement improvement programs for sustainable agriculture. Eight contrasting inbred lines were used to obtain simple hybrids for diallel analysis. Twenty-eight diallelic hybrids plus the popcorn parental lines were evaluated at two different sites under two contrasting environments for soil phosphorus availability (6 × 6 lattice design). Grain yield, popping expansion, and volume of expanded popcorn per hectare were measured. A combined analysis of variance and a test of means were performed. The classification and utilization of the phosphorus use efficiency index, according to the grain yield performance of the hybrids under contrasting environments, was considered. Through model 2 of the Griffing's diallel analysis method, the general and specific combining abilities were estimated, along with their environmental interactions. The best strategy to obtain genotypes that are efficient and responsive to phosphorus involves exploring popcorn hybrids using genitors that result in the accumulation of additive genes that promote popping expansion. Hybrids P7 × L80, P7 × L59, P7 × L76, and P6 × L80 presented promising results and may be evaluated as cultivation options in phosphorus-deficient soils., Competing Interests: The authors have declared that no competing interests exist.

The resistance to abiotic stress is increasingly recognised as being impacted by maternal effects, given that environmental conditions experienced by parent (mother) trees affect stress tolerance in offspring. We hypothesised that abiotic environmental maternal effects may also mediate the resistance of trees to biotic stress. The influence of maternal environment and maternal genotype and the interaction of these two factors on early resistance of Pinus pinaster half-sibs to the Fusarium circinatum pathogen was studied using 10 mother genotypes clonally replicated in two contrasting environments. Necrosis length of infected seedlings was 16% shorter in seedlings grown from favourable maternal environment seeds than in seedlings grown from unfavourable maternal environment seeds. Damage caused by F. circinatum was mediated by maternal environment and maternal genotype, but not by seed mass. Mechanisms unrelated to seed provisioning, perhaps of epigenetic nature, were probably involved in the transgenerational plasticity of P. pinaster, mediating its resistance to biotic stress. Our findings suggest that the transgenerational resistance of pines due to an abiotic stress may interact with the defensive response of pines to a biotic stress.