Modeling and Analysis of a Fractional Visceral Leishmaniosis with Caputo and Caputo–Fabrizio derivatives

Visceral leishmaniosis is one recent example of a global illness that demands our best efforts at understanding. Thus, mathematical modeling may be utilized to learn more about and make better epidemic forecasts. By taking into account the Caputo and Caputo-Fabrizio derivatives, a frictional model of visceral leishmaniosis was mathematically examined based on real data from Gedaref State, Sudan. The stability analysis for Caputo and Caputo-Fabrizio derivatives is analyzed. The suggested ordinary and fractional differential mathematical models are then simulated numerically. Using the Adams-Bashforth method, numerical simulations are conducted. The results demonstrate that the Caputo-Fabrizio derivative yields more precise solutions for fractional differential equations

A Symmetry Chaotic Model with Fractional Derivative Order via Two Different Methods

In this article, we have investigated solutions to a symmetry chaotic system with fractional derivative order using two different methods—the numerical scheme for the ABC fractional derivative, and the Laplace decomposition method, with help from the MATLAB and Mathematica platforms. We have explored progressive and efficient solutions to the chaotic model through the successful implementation of two mathematical methods. For the phase portrait of the model, the profiles of chaos are plotted by assigning values to the attached parameters. Hence, the offered techniques are relevant for advanced studies on other models. We believe that the unique techniques that have been proposed in this study will be applied in the future to build and simulate a wide range of fractional models, which can be used to address more challenging physics and engineering problems

A Comparative Numerical Study of the Symmetry Chaotic Jerk System with a Hyperbolic Sine Function via Two Different Methods

This study aims to find a solution to the symmetry chaotic jerk system by using a new ABC-FD scheme and the NILM method. The findings of the supplied methods have been compared to Runge–Kutta’s fourth order (RK4). It was discovered that the suggested techniques gave results comparable to the RK4 method. Our primary goal is to develop effective methods for addressing symmetrical, chaotic systems. Using ABC-FD and NILM presents innovative approaches for comprehending and effectively handling intricate dynamics. The findings of this study have significant significance for addressing the occurrence of chaotic behavior in diverse scientific and engineering contexts. This research significantly contributes to fractional calculus and its various applications. The application of ABC-FD, which can identify chaotic behavior, makes our work stand out. This novel approach contributes to advancing research in nonlinear dynamics and fractional calculus. The present study not only offers a resolution to the problem of symmetric chaotic jerk systems but also presents a framework that may be applied to tackle analogous challenges in several domains. The techniques outlined in this paper facilitate the development and computational analysis of prospective fractional models, thereby contributing to the progress of scientific and engineering disciplines

Analysis, modeling and simulation of a fractional-order influenza model

The primary goal of this study is to provide a novel mathematical model for Influenza using the Atangana–Baleanu Caputo fractional-order derivative operator (ABC-Operator) in place of the standard operator. There will be an examination of how the influenza-positive solutions reacts to real-world data. The fractional Euler Method will be utilized to reveal the dynamics of the influenza mathematical model. Both the stability of the disease-free equilibrium and the endemic equilibrium points, two symmetrical extrema of the proposed dynamical model, are examined. It will be shown, using numerical comparisons, that the findings obtained by employing the fractional-order model are considerably more similar to certain actual data than the integer-order model's results. These should shed light on the significance of fractional calculus when confronting epidemic risks

Exploring analytical results for (2+1) dimensional breaking soliton equation and stochastic fractional Broer-Kaup system

This paper introduces a pioneering exploration of the stochastic (2+1) dimensional breaking soliton equation (SBSE) and the stochastic fractional Broer-Kaup system (SFBK), employing the first integral method to uncover explicit solutions, including trigonometric, exponential, hyperbolic, and solitary wave solutions. Despite the extensive application of the Broer-Kaup model in tsunami wave analysis and plasma physics, existing literature has largely overlooked the complexity introduced by stochastic elements and fractional dimensions. Our study fills this critical gap by extending the traditional Broer-Kaup equations through the lens of stochastic forces, thereby offering a more comprehensive framework for analyzing hydrodynamic wave models. The novelty of our approach lies in the detailed investigation of the SBSE and SFBK equations, providing new insights into the behavior of shallow water waves under the influence of randomness. This work not only advances theoretical understanding but also enhances practical analysis capabilities by illustrating the effects of noise on wave propagation. Utilizing MATLAB for visual representation, we demonstrate the efficiency and flexibility of our method in addressing these sophisticated physical processes. The analytical solutions derived here mark a significant departure from previous findings, contributing novel perspectives to the field and paving the way for future research into complex wave dynamics

Effect of Salvadora persica (Miswak) leaves and stem aqueous extracts on ovarian folliculogenesis and uterine histology in female albino rats

This work was conducted to evaluate the antifertility activities of Salvadora persica (miswak) aqueous leaves and stem extracts  on female albino Wistar rats. Control animals received 0.5 ml of distilled water (Group 1); experimental animals received 0.5 ml of aqueous solution (1:1 w/v) of miswak leaves (Group2) or stem extract (Group 3) for 14 consecutive days. At the end of experiment, animals were weighed and vaginal smears were obtained from control and treated groups. Control and experimental animals were anesthetized then scarified, ovaries and uterus were dissected out, weighed and the number of corpora lutea and surface ovarian follicles were counted. Ovaries and uterus were fixed then processed for paraffin sections and stained with Hematoxylin-eosin. Histological changes in ovaries and uterus were determined. Results showed that administration of miswak leaves or stem aqueous extract is safe and have no side effects or mortalities, and it did not affect body weight of treated animals compared with control. However, administration of miswak leaves or stem aqueous extract significantly decrease (P<0.05) ovarian weight in treated groups. Uterine weight also significantly decreased (P<0.05) after administration of miswak leaves extract compared to control or stem extract groups. Moreover, number of surface ovarian follicles significantly decreased (P<0.05) after exposure to extract of miswak leaves or stem. Number of corpora lutea did not vary between groups. Histological examination revealed that administration of miswak leaves extract caused a significant decrease in the epithelial cell height, myometrial and stromal thickness of uterus compared to stem extract or control group. The present study illustrated the antiovulatory and anti-uterotrophic effects of the aqueous extract of miswak leaves in female rats. This effect may be mediated through direct effect of the extract on the reproductive organs by disruption of ovarian folliculogenesis and inhibiting further development of the recruited ovarian follicles and/or by disruption of the hormonal balance in the hypothalamo-hypophysial ovarian and uterine axis. Miswak stem extract could affect follicular development but it did not affect the uterine structures

General Methods to Synchronize Fractional Discrete Reaction–Diffusion Systems Applied to the Glycolysis Model

Because they are useful for both enabling numerical simulations and containing well-defined physical phenomena, discrete fractional reaction–diffusion models have attracted a great deal of interest from academics. Within the family of fractional reaction–diffusion models, a discrete form is examined in detail in this study. Furthermore, we investigate the complex synchronization dynamics of a suggested discrete master–slave reaction–diffusion system using the accuracy of linear control techniques combined with a fractional discrete Lyapunov approach. This study’s deviation from the behavior of equivalents with integer orders makes it very fascinating. Like the non-local nature inherent in Caputo fractional derivatives, it creates a memory Lyapunov function that is closely linked to the historical background of the system. The investigation provides a strong basis to the theoretical results

Effect of Salvadora persica (Miswak) leaves and stem aqueous extracts on ovarian folliculogenesis and uterine histology in female albino rats

This work was conducted to evaluate the antifertility activities of Salvadora persica (miswak) aqueous leaves and stem extracts  on female albino Wistar rats. Control animals received 0.5 ml of distilled water (Group 1); experimental animals received 0.5 ml of aqueous solution (1:1 w/v) of miswak leaves (Group2) or stem extract (Group 3) for 14 consecutive days. At the end of experiment, animals were weighed and vaginal smears were obtained from control and treated groups. Control and experimental animals were anesthetized then scarified, ovaries and uterus were dissected out, weighed and the number of corpora lutea and surface ovarian follicles were counted. Ovaries and uterus were fixed then processed for paraffin sections and stained with Hematoxylin-eosin. Histological changes in ovaries and uterus were determined. Results showed that administration of miswak leaves or stem aqueous extract is safe and have no side effects or mortalities, and it did not affect body weight of treated animals compared with control. However, administration of miswak leaves or stem aqueous extract significantly decrease (P<0.05) ovarian weight in treated groups. Uterine weight also significantly decreased (P<0.05) after administration of miswak leaves extract compared to control or stem extract groups. Moreover, number of surface ovarian follicles significantly decreased (P<0.05) after exposure to extract of miswak leaves or stem. Number of corpora lutea did not vary between groups. Histological examination revealed that administration of miswak leaves extract caused a significant decrease in the epithelial cell height, myometrial and stromal thickness of uterus compared to stem extract or control group. The present study illustrated the antiovulatory and anti-uterotrophic effects of the aqueous extract of miswak leaves in female rats. This effect may be mediated through direct effect of the extract on the reproductive organs by disruption of ovarian folliculogenesis and inhibiting further development of the recruited ovarian follicles and/or by disruption of the hormonal balance in the hypothalamo-hypophysial ovarian and uterine axis. Miswak stem extract could affect follicular development but it did not affect the uterine structures

Mosquito vectors survey in the AL-Ahsaa district of eastern Saudi Arabia

The present study aimed to identify the mosquito vectors distributed throughout AL-Ahsaa district situated in the eastern region of Saudi Arabia. Mosquito larvae were collected seasonally for one year (October 2009 to September 2010) from different breeding sites in seven rural areas utilizing long aquatic nets. Salinity and pH of these breeding sites were also measured seasonally. The survey revealed the presence of five mosquito species, Aedes caspius Pallas (Diptera: Culicidae), Anopheles multicolor Cambouliu, Culex perexiguus Theobald, Culex pipiens L., and Culex pusillus Macquart, representing three genera; four of them (Ae. caspius, An. multicolor, Cx. perexiguus, and Cx. pipiens) are important vectors of diseases. Ae. caspius is the most common vector followed by Cx. pipiens and then Cx. perexiguus. Mosquitoes in AL-Ahsaa are prevalent in both winter and spring seasons, rarely encountered in summer, and are found in moderation during the autumn months. These results are compared with results of other regions in the Kingdom of Saudi Arabia

Mathematical modeling and stability analysis of the novel fractional model in the Caputo derivative operator: A case study

The fundamental goal of this research is to suggest a novel mathematical operator for modeling visceral leishmaniasis, specifically the Caputo fractional-order derivative. By utilizing the Fractional Euler Method, we were able to simulate the dynamics of the fractional visceral leishmaniasis model, evaluate the stability of the equilibrium point, and devise a treatment strategy for the disease. The endemic and disease-free equilibrium points are studied as symmetrical components of the proposed dynamical model, together with their stabilities. It was shown that the fractional calculus model was more accurate in representing the situation under investigation than the classical framework at α = 0.99 and α = 0.98. We provide justification for the usage of fractional models in mathematical modeling by comparing results to real-world data and finding that the new fractional formalism more accurately mimics reality than did the classical framework. Additional research in the future into the fractional model and the impact of vaccinations and medications is necessary to discover the most effective methods of disease control