In this work, we investigate the invariance properties of nonlinear fractional partial differential equations (NLFPDEs) involving conformable fractional derivatives in both spatial and temporal variables by employing the framework of Lie symmetry analysis. Specifically, the study focuses on the generalized modified Burgers equation and the generalized modified Kortewegde Vries (mKdV) equation with conformable fractional derivatives. The corresponding infinitesimal generators and symmetry vector fields for both the models are systematically derived. Then by using these Lie symmetries, the governing equations are transformed into ordinary differential equations. To obtain exact analytical solutions, the ansatz methods and the (F/G)-expansion technique is applied on the reduced equations. Furthermore, the generalized mKdV equation is transformed into an autonomous dynamical system, enabling a qualitative investigation through bifurcation theory.

This study employs the Lie symmetry technique to explore the symmetry features of the time fractional Kupershmidt equation. Specifically, we use the Lie symmetry technique to derive the symmetry generators for this equation, which incorporates a conformal fractional derivative. We use the symmetry generators to transform the fractional partial differential equation into a fractional ordinary differential equation, thereby simplifying the analysis. The obtained reduced equation is of fourth order nonlinear ordinary differential equation. To find the wave solutions, F/G-expansion process has been used to obatin different types of solutions of the time-fractional Kuperschmidt equation. The obtained wave solutions are hyperbolic and trigonometric in nature. We then use Maple software to visually depict these wave solutions for specific parameter values, providing insights into the behaviour of the system under investigation. Peak and kink wave solutions are achieved for the given problem.

Abstract Induction motors are in high demand for industrial applications due to their reliable and efficient performance compared to other electrical motors. Therefore, the implementation of a predictive maintenance scheme is necessary to minimise financial losses in terms of revenue and maintenance costs. This scheme involves health monitoring system, aimed to enhance motor reliability, extend their useful lifespan and reduce maintenance expenses. Furthermore, traditional health monitoring systems often involve human intervention, which can slow down the diagnosis process. Therefore, a self-sufficient automated system has evolved to improve motor performance and reliability. This paper presents a comprehensive study of induction motor failures and the various methods used for their diagnosis. Additionally, it also discussed the importance of predictive maintenance and the pivotal role played by automated systems in ensuring the sustained efficiency of induction motors in industrial settings.

In recent work, travelling wave solutions of the time fractional simple modified Kawahara equation have been obtained using the F/G -expansion method. The wave transformation is acquired by Lie symmetry analysis with conformal fractional derivatives. The nonlinear partial differential equation (NLPDE) is transformed into an ordinary differential equation (ODE) of fractional order, making use of wave transformation. Also, the series solution of the reduced ODE is attained. Some graphs of the acquired solutions are drawn using Maple.

This paper studies symmetry reductions of time fractional K(m,1) equation with generalized evolution which is one of the important equation in fractional partial differential equations (FPDEs). Here, the classical Lie symmetries are obtained and utilized for the reduction of time fractional K(m,1) equation into ordinary differential equations. Some new exact solutions are obtained which are in the form of solitary waves by using G′G-expansion method and one of the obtained solutions is acceptable for qualitative analysis. By showing the phase portraits, its dynamical behaviour is further completely explained.

The purpose of this article to study the conformal derivative form of nonlinear fractional partial differential equation. The time fractional generalized KdV-mKdV equation with higher order nonlinear terms is taken to utlize the concept of conformal derivative and Leibnitz rule for finding the wave solutions. The theory of bifurcation analysis is applied for the qualitative analysis of this equation to study the stability nature at the different critical points. The solutions obtained by the method of G^'/G represents graphically. The numerical classical Runge Kutta fourth order technique is implemented computationally to manifest the results which shows a good agreement with the obtained analytical solutions.

Background: Cancer is the second leading cause of death globally, accounting for an estimated 9.6 million deaths, or one in six deaths, in 2018. Lung, prostate, colorectal, stomach, and liver cancers are the most common types of cancer in men, while breast, colorectal, lung, cervical, and thyroid cancers are the most common among women. The present study attempts to determine the various factors associated with lung cancer in Indian settings. Objectives: This study aimed to study various epidemiological and environmental risk factors associated with lung cancer and making suitable recommendations. Materials and Methods: The present study is a case–control study and carried out at a tertiary care hospital of India. The population comprised patients attending the hospital for any of their disease conditions. The sample size was calculated as 68 cases and 68 controls. The duration of study was January 2015–June 2017. Ethical clearance was obtained from the college institutional ethics committee before the start of the study. Informed consent was obtained from each subject before the conduct of the study. Data collection was done by a pretested and prestructured questionnaire. Data entry and analysis was entered by researcher and analyzed using SPSS version 20 software. Results: On analysis, it was found that the use of tobacco product, duration of incense stick use, and fuel used for cooking food or heating significantly associated with lung cancer. Conclusions: The study concluded in bringing out the various epidemiological and other environmental risk factors causing lung cancer.

In the present article, the time fractional Fisher equation is considered in conformal form to study the application of the Lie classical method and quantitative analysis. The Lie symmetry method has been applied to find the infinitesimal generators and symmetry reductions of the fractional Fisher equation. The obtained reduced form of the equation is solved by the method of G′/G, which gives different forms of solutions. The theory of bifurcation has been utilized in the reduced form to check the stability and nature of critical points by transforming the equations into an autonomous system. Some phase portraits have been drawn at different critical points by the use of maple.

In this current study, a systematic investigation is carried to derive symmetry reductions of conformable time-fractional Schamel–KdV equation via the Lie symmetry method. Using the obtained Lie point symmetries of nonlinear fractional partial differential equation, the symmetry reduction is generated and utilized that for reduction into an ordinary differential equation. Some solutions of the reduced fractional ordinary differential equation are found with two straightforward methods to study its traveling wave solutions and series solutions respectively. The method helps to obtain solutions in the form of trigonometric, hyperbolic and rational functions. Also, we have presented some figures for the obtained explicit solutions that helps us in physical interpretation of equation.

This paper uses the classical Lie symmetry method for optical solitons to study the Chen-Lee-Liu equation. We are able to establish symmetries that convert the model into a set of ordinary differential equations and obtain solutions of the reduced equations through various methods.

Oligomerization of YsaN, a putative T3SS-ATPase is a necessary and crucial event for T3SS functioning in Y. enterocolitica. Different oligomeric states have been proposed for similar ATPases, yet, the true nature of its activation and formation of different oligomers is still poorly understood. In-vitro studies of YsaN reveal that its activation and oligomerization depend on its N-terminal region and occur as a result of active catalysis of ATP in an ATP concentration-dependent manner following two-step cooperative kinetics. Also, the N-terminal 83 amino acid residues of YsaN are crucial for higher-order oligomer formation while YsaN∆83 is capable of hexamer formation upon oligomerization. Enzyme kinetics study shows reduced ATPase activity of YsaN∆83 (3.19 ± 0.09 μmol/min/mg) in comparison to YsaN (9.076 ± 0.72 μmol/min/mg). Negative-TEM study of YsaN and YsaN∆83 oligomer suggests that the formation of higher-order oligomer (probably dodecamer) occurs by stacking of two hexamers through their N-terminal faces involving N-terminal 83 amino acid residues which have been further supported by the docking of two hexamers during the in-silico study. These results suggest that YsaN is an oligomerization-activated T3SS ATPase, where distinct regions of its N-terminal domain regulate its different oligomeric nature and is essential for its activation.

In enteropathogen, Yersinia enterocolitica , the genes encoding phage shock proteins are organized in an operon ( pspA-E ), which is activated at the various types of cellular stress (i.e., extracytoplasmic or envelop stress) whereas, PspA negatively regulates PspF, a transcriptional activator of pspA-E and pspG , and is also involved in other cellular machinery maintenance processes. The exact mechanism of association and dissociation of PspA and PspF during the stress response is not entirely clear. In this concern, we address conformational change of PspA in different pH conditions using various in-silico and biophysical methods. At the near-neutral pH, CD and FTIR measurements reveal a ß-like conformational change of PspA; however, AFM measurement indicates the lower oligomeric form at the above-mentioned pH. Additionally, the results of the MD simulation also support the conformational changes which indicate salt-bridge strength takes an intermediate position compared to other pHs. Furthermore, the bio-layer interferometry study confirms the stable complex formation that takes place between PspA and PspF at the near-neutral pH. It, thus, appears that PspA conformational change in adverse pH conditions abandons PspF from having a stable complex with it, and thus, the latter can act as a trans-activator. Taken together, it seems that PspA alone can transduce adverse signals by changing its conformation.

Background: Modafinil is a CNS stimulant used to treat Narcolepsy, sleepiness and other disorders related to sleep. It is a BCS class II drug having poor aqueous solubility. Objective: This study was aimed to formulate and evaluate orodispersible tablets of containing co-crystals of Modafinil for the improvisation of critical attributes of the product such as dissolution rates, solubility and oral bioavailability. Methods: Co-crystals were prepared by dry grinding method using Sodium acetate, Nicotinic acid, Benzoic acid, Urea and Succinic acetate as co-formers. Tablets were compressed by using direct compression method using SSG, Crospovidone, and Croscarmellose sodium as super disintegrants in different concentration. Results: Pre-formulation studies were performed and evaluation of prepared co-crystals revealed that Co-crystals formulated with sodium acetate showed best results. The manufactured orodispersible tablets were evaluated for different parameters including weight variation, hardness, thickness, friability, drug content, In-vitro disintegration and In-vitro dissolution studies. Formulation F2 shows significant change in dissolution rate and also helped to increase the solubility of poorly water soluble drugs and both of them i.e. solubility and percentage of drug release are the key factors to exhibit the efficiency of the drug. Formulation of co-crystal with sodium acetate in 1:1 ratio showed highest drug content (97.97%), while Benzoic acid in ratio 1:2 showed least drug content (56.48%). Conclusion: According to the result obtained, an orodispersible tablet containing co-crystals of modafinil enhances the dissolution rate, solubility and hence increases the therapeutic efficacy and could be considered convenient oral delivery systems to enhance the drug bioavailability. Keywords: Co-crystal, Oro-dispersible, Sodium acetate, Narcolepsy, Sleepiness

In this article, an attempt is made to achieve the series solution of the time fractional generalized Korteweg-de Vries equation which leads to a conditionally convergent series solution. We have also resorted to another technique involving conversion of the given fractional partial differential equations to ordinary differential equations by using fractional complex transform. This technique is discussed separately for modified Riemann-Liouville and conformable derivatives. Convergence analysis and graphical view of the obtained solution are demonstrated in this work.

In this article, the variable-coefficients form of Extended Ostrovsky Equation is considered for the Painlevé analysis and Lie group analysis for finding the symmetries by the using Lie classical approach. It is proved that only in some cases, the corresponding traveling wave equation and exact solutions of the obtained reduced form ordinary differential equations are determined by using extended $$\frac{G^{'}}{{G}}$$ -expansion method and tanh method. The nonlinear behaviour of the solutions is represented with the formation of different types of graphs.

Lifetimes of states in the negative-parity band, based on the $$\nu (h_{11/2})$$ orbital in $$^{103}\hbox {Pd}$$ , have been measured in the spin range from 27/2 to 39/2 using the Doppler-Shift Attenuation Method. The inferred B(E2) values are observed to decrease with increasing angular momentum and $${\mathcal {J}}^{\text {(}2\text {)}}/$$ B(E2) values are found to be large (> 300 $$\hbar ^2\hbox {MeV}^{-1}\hbox {(eb)}^{-2}$$ ). These observations along with calculations based on the semiclassical particle-rotor model approach suggest that antimagnetic and collective rotation, along with gradual neutron alignment are responsible for angular momentum generation in the band under consideration.

Background: High levels of stress and psychological morbidity occur in health-care professional students. Objective: The objective of this study was to estimate psychological well-being, perceived stress level, and coping abilities among medical and paramedical students. Materials and Methods: A cross-sectional analytical study carried out in a tertiary care hospital, West Uttar Pradesh, India. The total study period was from September 2019 to November 2019 with a sample of 145 medical students aged 17–25 years and 81 paramedical students aged 19–33 years. Ethical clearance was obtained from the College Ethical Committee. We used self-administered, three different types of validated tools for data collection. Data were analyzed using SPSS Version 20. Results: The median age of paramedical and medical trainees was 22 and 21 years, respectively. Family history of mental illness was 21% and 5.5%, respectively. On general health questionnaire-12 scale, 9% of paramedical trainees reported evidence of distress and 91% of severe problem and psychological distress while 19% of medical trainees having evidence of distress and 81% of severe problem and psychological distress. On perceived stress scale-10 (PSS-10) scale, 15% of paramedical trainees reported average level, 27% moderate level, and 55% high level of perceived stress while 2% of medical trainees having average, 19% moderate level, and 79% high level of perceived stress, respectively. The difference in mean score on PSS-10 and Brief COPE scale between paramedics and medical trainees group was found statistically significant (P < 0.05). Conclusion: We concluded the higher level of severe problem and psychological distress in the paramedical and high level of perceived stress in medical trainees. Paramedical trainees practice a better coping mechanism than medical trainees.