General Closed Form Wave Solutions of Nonlinear Space-Time Fractional Differential Equation in Nonlinear Science

We have enucleated new and further exact general wave solutions, along with multiple exact traveling wave solutions of space-time nonlinear fractional Chan-Hillard equation, by applying a relatively renewed technique two variables -expansion method. Also, based on fractional complex transformation and the properties of the modified Riemann-Liouville fractional order operator, the fractional partial differential equations are transforming into the form of ordinary differential equation. This method can be rumination of as the commutation of well-appointed -expansion method introduced by M. Wang et al.. In this paper, it is mentioned that the two variables - expansion method is more legitimate, modest, sturdy and effective in the sense of theoretical and pragmatical point of view. Lastly, by treating computer symbolic program Mathematica, the uniqueness of our attained wave solutions are represented graphically and reveal a comparison in a submissive manner

Mathematical modeling on the transmission of COVID-19 and its reproduction numbers in SAARC countries

In the middle of December 2019, a virus known as coronavirus (COVID-19) generated by severe acute respiratory syndrome corona virus 2 (SARC-CoV-2) was first detected in Wuhan, Hubei Province, China. As of the 9th of March, 2022, spread to over 212 countries, causing 429 million confirmed cases and 6 million people to lose their lives worldwide. In developing countries like the South Asian area, alarming dynamic variations in the pattern of confirmed cases and death tolls were displayed. During epidemics, accurate assessment of the characteristics that characterize infectious disease transmission is critical for optimizing control actions, planning, and adapting public health interventions. The reproductive number, or the typical number of secondary cases caused by an infected individual, can be employed to determine transmissibility. Several statistical and mathematical techniques have been presented to calculate across the duration of an epidemic. A technique is provided for calculating epidemic reproduction numbers. It is a MATLAB version of the EpiEstim package's R function estimate R, version 2.2-3. in the South Asian Association for Regional Cooperation (SAARC) countries. The three methodologies supported are 'parametric SI,' 'non-parametric SI,' and 'uncertain SI.' The present study indicated that the highest reproduction number was 12.123 and 11.861 on 5th and 14th March 2020 in India and Sri_Lanka, whereas the lowest reproduction number was the lowest was 0.300 and 0.315 in Sri_Lanka and India. The Maximum and minimum reproductive number of Bangladesh was 3.752 and 0.725. In this study, we have tried to point out the worst, best and current situation of SAARC countries

Estimation of the SARS-CoV-2 specific reproduction number in SAARC countries: A 60-days Data-driven analysis

Novel coronavirus disease-2019 (COVID-19) was acknowledged as a global pandemic by WHO, which was first observed at the end of December 2019 in Wuhan city, China, caused by extreme acute respiratory syndrome coronavirus2 (SARS-CoV-2). According to the Weekly operation Update on COVID-19 (November 13, 2020) of the World Health Organization, more than 53 million confirmed cases are reported, including 1.3 million deaths. Various precautionary measures have been taken worldwide to reduce its transmission, and extensive researches are going on. The purpose of this analysis was to determine the initial number of reproductions (Ro) of the coronavirus of SAARC countries named Afghanistan, Bangladesh, India, Pakistan, Bhutan, Nepal, the Maldives, and Sri-Lanka for the first 60 days as the growth is exponential in the early 60 days. The reproduction numbers of coronavirus for Afghanistan, Bangladesh, India, Pakistan, Bhutan, the Maldives, Nepal, and Sri Lanka are 1.47, 3.86, 2.07, 1.43, 1.31, 3.22, 1.75, and 2.39 respectively. The basic reproduction number (R0) 3.86 for Bangladesh and 1.31 for Bhutan indicated that up to 60-days of the outbreak COVID-19, the epidemic was more severe in Bangladesh and less severe in Bhutan among all the SAARC countries. Our predictions can be helpful in planning alertness and taking the appropriate measures to monitor it

New applications of the fractional derivative to extract abundant soliton solutions of the fractional order PDEs in mathematics physics

The motive of this research work is to unravel the mysteries of nature through fractional-order partial differential equations (PDEs). Here, we focus on two important fractional order nonlinear PDEs, namely the fractional order (4+1)-dimensional Fokas equation, which is used to give the model of many physical phenomena and dynamical processes, and the other one is the fractional order (2+1)-dimensional breaking soliton equation which is used to analyze the nonlinear problems like optical fiber communications, ocean engineering, etc. Recently, it has been an essential topic to extract the new soliton solutions which are used to investigate the hidden physical conditions of the nonlinear fractional PDEs. So, it is essential to solve those nonlinear fractional PDEs which have a physical impact in the fields of science and modern engineering. In our investigation, we attempt to provide nonlinear wave propagation patterns and investigate the equations, as mentioned earlier, through a computational method. A computing operating software called Mathematica has been applied to get a clear visualization of our gained outcomes, and we ascertain such types of shapes as the bell shape soliton, the anti-bell shape soliton, the singular bell shape soliton, the periodic solution, and the singular periodic solution. Our obtained results can keep an indispensable role in explaining various physical phenomena of nature shortly, and the applied method is the very cogent, efficient, and interesting to extract such types of solutions. Since we extract abundant solutions of these models, so we hope that this article is the best applications of mention method

In vitro antioxidant and cholinesterase inhibitory activities of Elatostema papillosum leaves and correlation with their phytochemical profiles: a study relevant to the treatment of Alzheimer’s disease

Abstract Background Alzheimer’s disease (AD), one of the major causes of dementia, is an overwhelming neurodegenerative disease that particularly affects the brain, leading to memory loss and impairment of language and judgment capacity. The aim of the present study was to investigate the antioxidant and anticholinesterase properties of the leaves of Elatostema papillosum (EPL) and correlate with their phytochemical profiles, which are relevant to the treatment of AD. Methods The dried coarse powder of EPL was extracted with 80% methanol (EPL-M80) by cold extraction method. The resultant EPL-M80 was assessed for acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) inhibitory activity by the Ellman method. The antioxidant activity was determined by DPPH (1, 1-diphenyl-2-picrylhydrazyl) and hydroxyl radical scavenging assays. Quantitative phytochemical (phenolic and flavonoid contents) analysis of endogenous substances in EPL-M80 was performed by standard spectrophotometric methods. Results EPL-M80 significantly (p < 0.05) inhibited AChE and BChE activity with IC50 of 165.40 ± 4.01 and 213.81 ± 3.57 μg/mL, respectively in a dose-dependent manner. Additionally, EPL-M80 exhibited strong radical scavenging activity against DPPH (IC50 = 32.35 ± 0.68 μg/mL) and hydroxyl radical (IC50 = 19.67 ± 1.42 μg/mL) when compared to that of standards. EPL-M80 was found to be rich in phenolic (23.74 mg gallic acid equivalent/g of dry extract) and flavonoid (31.18 mg quercetin equivalent/g of dry extract) content. Furthermore, a positive correlation (p < 0.001) was observed between the total phenolics and antioxidant as well as the anticholinesterase potential. Conclusions The marked inhibition of AChE and BChE, and potent antioxidant activity of the leaves of Elatostema papillosum highlight its potential to provide an effective treatment for AD