Novel Investigation of Stochastic Fractional Differential Equations Measles Model via the White Noise and Global Derivative Operator Depending on Mittag-Leffler Kernel

Because of the features involved with their varied kernels,differential operators relying on convolution formulations have been acknowledged as effective mathematical resources for modeling real-world issues.In this paper,we constructed a stochastic fractional framework of measles spreading mechanisms with dual medication immunization considering the exponential decay and Mittag-Leffler kernels.In this approach,the overall population was separated into five cohorts.Furthermore,the descriptive behavior of the system was investigated,including prerequisites for the positivity of solutions,invariant domain of the solution,presence and stability of equilibrium points,and sensitivity analysis.We included a stochastic element in every cohort and employed linear growth and Lipschitz criteria to show the existence and uniqueness of solutions.Several numerical simulations for various fractional orders and randomization intensities are illustrated.

A New Scheme of the ARA Transform for Solving Fractional-Order Waves-Like Equations Involving Variable Coefficients

The goal of this research is to develop a new,simplified analytical method known as the ARA-residue power series method for obtaining exact-approximate solutions employing Caputo type fractional partial differential equations(PDEs)with variable coefficient.ARA-transform is a robust and highly flexible generalization that unifies several existing transforms.The key concept behind this method is to create approximate series outcomes by implementing the ARA-transform and Taylor’s expansion.The process of finding approximations for dynamical fractional-order PDEs is challenging,but the ARA-residual power series technique magnifies this challenge by articulating the solution in a series pattern and then determining the series coefficients by employing the residual component and the limit at infinity concepts.This approach is effective and useful for solving a massive class of fractional-order PDEs.Five appealing implementations are taken into consideration to demonstrate the effectiveness of the projected technique in creating solitary series findings for the governing equations with variable coefficients.Additionally,several visualizations are drawn for different fractional-order values.Besides that,the estimated findings by the proposed technique are in close agreement with the exact outcomes.Finally,statistical analyses further validate the efficacy,dependability and steady interconnectivity of the suggested ARA-residue power series approach.

Dynamical Analysis of the Stochastic COVID-19 Model Using Piecewise Differential Equation Technique

Various data sets showing the prevalence of numerous viral diseases have demonstrated that the transmission is not truly homogeneous.Two examples are the spread of Spanish flu and COVID-19.The aimof this research is to develop a comprehensive nonlinear stochastic model having six cohorts relying on ordinary differential equations via piecewise fractional differential operators.Firstly,the strength number of the deterministic case is carried out.Then,for the stochastic model,we show that there is a critical number RS0 that can predict virus persistence and infection eradication.Because of the peculiarity of this notion,an interesting way to ensure the existence and uniqueness of the global positive solution characterized by the stochastic COVID-19 model is established by creating a sequence of appropriate Lyapunov candidates.Adetailed ergodic stationary distribution for the stochastic COVID-19 model is provided.Our findings demonstrate a piecewise numerical technique to generate simulation studies for these frameworks.The collected outcomes leave no doubt that this conception is a revolutionary doorway that will assist mankind in good perspective nature.

Does sevoflurane sedation in pediatric patients lead to“pseudo”leptomeningeal enhancement in the brain on 3 Tesla magnetic resonance imaging?

BACKGROUND Prominent leptomeningeal contrast enhancement(LMCE)in the brain is observed in some pediatric patients during sedation for imaging.However,based on clinical history and cerebrospinal fluid analysis,the patients are not acutely ill and do not exhibit meningeal signs.Our study determined whether sevoflurane inhalation in pediatric patients led to this pattern of‘pseudo’LMCE(pLMCE)on 3 Tesla magnetic resonance imaging(MRI).AIM To highlight the significance of pLMCE in pediatric patients undergoing enhanced brain MRI under sedation to avoid misinterpretation in reports.METHODS A retrospective cross-sectional evaluation of pediatric patients between 0-8 years of age was conducted.The patients underwent enhanced brain MRI under inhaled sevoflurane.The LMCE grade was determined by two radiologists,and interobserver variability of the grade was calculated using Cohen’s kappa.The LMCE grade was correlated with duration of sedation,age and weight using the Spearman rho rank correlation.RESULTS A total of 63 patients were included.Fourteen(22.2%)cases showed mild LMCE,48(76.1%)cases showed moderate LMCE,and 1 case(1.6%)showed severe LMCE.We found substantial agreement between the two radiologists in detection of pLMCE on post-contrast T1 imaging(kappa value=0.61;P<0.001).Additionally,we found statistically significant inverse and moderate correlations between patient weight and age.There was no correlation between duration of sedation and pLMCE.CONCLUSION pLMCE is relatively common on post-contrast spin echo T1-weighted MRI of pediatric patients sedated by sevoflurane due to their fragile and immature vasculature.It should not be misinterpreted for meningeal pathology.Knowing pertinent clinical history of the child is an essential prerequisite to avoid radiological overcalling and the subsequent burden of additional investigations.

Analysis and Numerical Computations of the Multi-Dimensional,Time-Fractional Model of Navier-Stokes Equation with a New Integral Transformation

The analytical solution of the multi-dimensional,time-fractional model of Navier-Stokes equation using the triple and quadruple Elzaki transformdecompositionmethod is presented in this article.The aforesaidmodel is analyzed by employing Caputo fractional derivative.We deliberated three stimulating examples that correspond to the triple and quadruple Elzaki transform decomposition methods,respectively.The findings illustrate that the established approaches are extremely helpful in obtaining exact and approximate solutions to the problems.The exact and estimated solutions are delineated via numerical simulation.The proposed analysis indicates that the projected configuration is extremely meticulous,highly efficient,and precise in understanding the behavior of complex evolutionary problems of both fractional and integer order that classify affiliated scientific fields and technology.

New Computation of Unified Bounds via a More General Fractional Operator Using Generalized Mittag-Leffler Function in the Kernel

In the present case,we propose the novel generalized fractional integral operator describing Mittag-Leffler function in their kernel with respect to another function Φ.The proposed technique is to use graceful amalgamations of the Riemann-Liouville(RL)fractional integral operator and several other fractional operators.Meanwhile,several generalizations are considered in order to demonstrate the novel variants involving a family of positive functions n(n∈N)for the proposed fractional operator.In order to confirm and demonstrate the proficiency of the characterized strategy,we analyze existing fractional integral operators in terms of classical fractional order.Meanwhile,some special cases are apprehended and the new outcomes are also illustrated.The obtained consequences illuminate that future research is easy to implement,profoundly efficient,viable,and exceptionally precise in its investigation of the behavior of non-linear differential equations of fractional order that emerge in the associated areas of science and engineering.

New generalized fuzzy transform computations for solving fractional partial differential equations arising in oceanography

This paper presents a study of nonlinear waves in shallow water.The Korteweg-de Vries(KdV)equa-tion has a canonical version based on oceanography theory,the shallow water waves in the oceans,and the internal ion-acoustic waves in plasma.Indeed,the main goal of this investigation is to employ a semi-analytical method based on the homotopy perturbation transform method(HPTM)to obtain the numerical findings of nonlinear dispersive and fifth order KdV models for investigating the behaviour of magneto-acoustic waves in plasma via fuzziness.This approach is connected with the fuzzy generalized integral transform and HPTM.Besides that,two novel results for fuzzy generalized integral transforma-tion concerning fuzzy partial gH-derivatives are presented.Several illustrative examples are illustrated to show the effectiveness and supremacy of the proposed method.Furthermore,2D and 3D simulations de-pict the comparison analysis between two fractional derivative operators(Caputo and Atangana-Baleanu fractional derivative operators in the Caputo sense)under generalized gH-differentiability.The projected method(GHPTM)demonstrates a diverse spectrum of applications for dealing with nonlinear wave equa-tions in scientific domains.The current work,as a novel use of GHPTM,demonstrates some key differ-ences from existing similar methods.

Constructing analytical estimates of the fuzzy fractional-order Boussinesq model and their application in oceanography

The main idea of this article is the investigation of atmospheric internal waves,often known as gravity waves.This arises within the ocean rather than at the interface.A shallow fluid assumption is illustrated by a series of nonlinear partial differential equations in the framework.Because the waves are scattered over a wide geographical region,this system can precisely replicate atmospheric internal waves.In this research,the numerical solutions to the fuzzy fourth-order time-fractional Boussinesq equation(BSe)are determined for the case of the aquifer propagation of long waves having small amplitude on the surface of water from a channel.The novel scheme,namely the generalized integral transform(proposed by H.Jafari[35])coupled with the Adomian decomposition method(GIADM),is used to extract the fuzzy fractional BSe in R,Rn and(2nth)-order including gH-differentiability.To have a clear understanding of the physical phenomena of the projected solutions,several algebraic aspects of the generalized integral transform in the fuzzy Caputo and Atangana-Baleanu fractional derivative operators are discussed.The confrontation between the findings by Caputo and ABC fractional derivatives under generalized Hukuhara differentiability are presented with appropriate values for the fractional order and uncertainty parameters℘∈[0,1]were depicted in diagrams.According to proposed findings,hydraulic engineers,being analysts in drainage or in water management,might access adequate storage volume quantity with an uncertainty level.