The primary objective of the present study was to investigate the enhancement of heat transfer in a Jeffery–Hamel hybrid nanofluid through a porous medium, within stretching/shrinking and convergent/divergent channels. The Darcy–Forchheimer (DF) law was employed to model the flow and thermal behavior of the nanofluid. The governing system of equations was derived using appropriate transformations. Numerical computations were performed using the NDSolve method in Mathematica-11. Results are presented through numerical data and graphical representations, illustrating the effects of various physical parameters on the flow profiles. Key findings indicate that increasing the inertia coefficient and nanoparticle volume fraction accelerates the velocity of the nanofluid in both divergent and convergent channels. Furthermore, higher porosity and inertia coefficients lead to increased drag forces exerted by the channel. Jeffery–Hamel hybrid nanofluids are significantly enhanced by increasing nanoparticle volume fraction, inertia coefficient, porosity, and the presence of radiation and heat source parameters, with a notably higher rate observed in the case of an expanding channel compared to a contracting one.

Multiple sclerosis (MS) is a common neurological disorder that affects the central nervous system (CNS) and can cause lesions that spread over space and time. Our study proposes a mathematical model that illustrates the progression of the disease and its likelihood of recurrence. We use Caputo fractional-order (FO) derivative operators to represent non-negative solutions and to establish a steady-state point and basic reproductive number. We also employ functional analysis to prove the existence of unique solutions and use the Ulam-Hyres (UH) notion to demonstrate the stability of the solution for the proposed model. Furthermore, we conduct numerical simulations using an Euler-type numerical technique to validate our theoretical results. Our findings are presented through graphs that depict various behaviors of the model for different parameter values.

This paper extends the cholera human-to-human direct transmission model from a deterministic to a stochastic framework. This is expressed as mixed system of stochastic and deterministic differential equations. A Lyapunov function is created to investigate the global stability of the stochastic cholera epidemic, which shows the existence of global positivity of the solution using the theory of stopping time. We then find the threshold quantity of the extended stochastic cholera epidemic model. We derive a parametric condition ${\tilde{R}}_0$, and for additive white noise, we establish sufficient conditions for the extinction and the persistence of the cholera infection. Finally, for a suitable choice of the parameter of the system for ${\tilde{R}}_0$, we perform numerical simulations for both scenarios of extinction and persistence of the dynamic of the cholera infection.

The purpose of this article is to discuss some midpoint type HHF fractional integral inequalities and related results for a class of fractional operators (weighted fractional operators) that refer to harmonic convex functions with respect to an increasing function that contains a positive weighted symmetric function with respect to the harmonic mean of the endpoints of the interval. It can be concluded from all derived inequalities that our study generalizes a large number of well-known inequalities involving both classical and Riemann-Liouville fractional integral inequalities.

In this article, the meshfree radial basis function method based on the Gaussian function is proposed for some time-space dependent fractional order partial differential equation (PDE) models. These PDE models have significant applications in chemical engineering and physical science. Some main advantages of the proposed method are that it is easy to implement, and the output response is quick and highly accurate, especially in the higher dimension. In this method, the time-dependent derivative terms are treated by Caputo fractional derivative while space-dependent derivative terms are treated by Riesz, Riemann-Liouville, and Grünwald-Letnikov derivatives. The proposed method is tested on some numerical examples and the accuracy is analyzed by $\Vert L{\Vert }_{\mathrm{\infty }}$.

The multi-term time-fractional order diffusion-wave equation (MT-TFDWE) is an important mathematical model for processes exhibiting anomalous diffusion and wave propagation with memory effects. This article develops a robust numerical technique based on the Chebyshev collocation method (CCM) coupled with the Laplace transform (LT) to solve the time-fractional diffusion-wave equation. The CCM is utilized to discretize the spatial domain, which ensures remarkable accuracy and excellent efficiency in capturing the variations of spatial solutions. The LT is used to handle the time-fractional derivative, which converts the problem into an algebraic equation in a simple form. However, while using the LT, the main difficulty arises in calculating its inverse. In many situations, the analytical inversion of LT becomes a cumbersome job. Therefore, the numerical techniques are then used to obtain the time domain solution from the frequency domain solution. Various numerical inverse Laplace transform methods (NILTMs) have been developed by the researchers. In this work, we use the contour integration method (CIM), which is capable of handling complex inversion tasks efficiently. This hybrid technique provides a powerful tool for the numerical solution of the time-fractional diffusion-wave equation. The accuracy and efficiency of the proposed technique are validated through four test problems.