The emerging concept of hybrid nanofluids has grabbed the attention of researchers and scientists due to improved thermal performance because of their remarkable thermal conductivities. These fluids have enormous applications in engineering and industrial sectors. Therefore, the present research study examines thermal and mass transportation in hybrid nanofluid past an inclined linearly stretching sheet using the Maxwell fluid model. In the current problem, the hybrid nanofluid is engineered by suspending a mixture of aluminum oxide $A{l}_2{O}_3$ and copper $Cu$ nanoparticles in ethylene glycol. The fluid flow is generated due to the linear stretching of the sheet and the sheet is kept inclined at the angle $\zeta =\pi /6$ embedded in porous medium. The current proposed model also includes the Lorentz force, solar radiation, heat generation, linear chemical reactions, and permeability of the plate effects. Here, in the current simulation, the cylindrical shape of the nanoparticles is considered, as this shape has proven to be excellent for the thermal performance of the nanomaterials. The governing equations transformed into ordinary differential equations are solved using MATLAB bvp4c solver. The velocity field declines with increasing magnetic field parameter, Maxwell fluid parameter, volume fractions of nanoparticles, and porosity parameter but increases with growing suction parameter. The temperature drops with increasing magnetic field force and suction parameter values but increases with increasing radiation parameter and volume fraction values. The concentration profile increases with increasing magnetic field parameters, porosity parameters, and volume fractions but reduces with increasing chemical reaction parameters and suction parameters. It has been noted that the purpose of the inclusion of thermal radiation is to augment the temperature that is serving the purpose in the current work. The addition of Lorentz force slows down the speed of the fluid and raises the boundary layer thickness, which is visible in the current study. It has been concluded that, when heat generation parameters increase, the temperature field increases correspondingly for both nanofluids and hybrid nanofluids. The increase in the volume fraction of the nanoparticles is used to enhance the thermal performance of the hybrid nanofluid, which is evident in the current results. The current results are validated by comparing them with published ones.

Jeffrey-type dusty fluid flow, combined with the effects of Newtonian heating, plays a critical role in numerous engineering applications, particularly in

Fractional calculus has been a concept used to obtain new variants of some well-known integral inequalities. In this study, our main goal is to establish the new fractional Hermite–Hadamard, and Simpson’s type estimates by employing a differentiable function. Furthermore, a novel class of fractional integral related to prominent fractional operator (Caputo–Fabrizio) for differentiable convex functions of first order is proven. Then, taking this equality into account as an auxiliary result, some new estimation of the Hermite–Hadamard and Simpson’s type inequalities as generalization is presented. Moreover, few inequalities for concave function are obtained as well. It is observed that newly established outcomes are the extension of comparable inequalities existing in the literature. Additionally, we discuss the applications to special means, matrix inequalities, and the q-digamma function.

Fractional differential equations (FDEs) are employed to describe the physical universe. This article investigates the attractivity of solutions for FDEs and Ulam–Hyers–Rassias stability, involving the $\Psi$-Hilfer fractional derivative. Important results are presented using Krasnoselskii’s fixed point theorem, which provides a framework for analyzing the stability and attractivity of solutions. Novel results on the attractiveness of solutions to nonlinear FDEs in Banach spaces are derived, and the existence of solutions, stability properties, and behavior of system equilibria are examined. The application of $\Psi$-Hilfer fractional derivatives in modeling financial crises is explored, and a financial crisis model using $\Psi$-Hilfer fractional derivatives is proposed, providing more general and global results. Furthermore, we also perform a numerical analysis to validate our theoretical findings.

In this paper, we introduce and investigate a new class of special polynomials called degenerate Peter–Genocchi polynomials. We define these polynomials and their associated numbers via an explicit generating function and explore a variety of their fundamental algebraic and analytic properties. In particular, we derive summation formulas (expressing polynomials via their associated numbers), addition formulas (splitting the polynomial argument), an implicit summation formula (a bivariate convolution identity), and symmetric identities. We also establish connections with degenerate Stirling numbers of both kinds, higher-order degenerate Genocchi polynomials, and higher-order degenerate Daehee polynomials. Furthermore, we investigate derivative properties and present a differential operator formula. Finally, we provide tables of approximate zeros and graphical representations of the zeros in the complex plane.

This paper studied the Cauchy problem for a system of coupled Korteweg-de Vries (KdV) equations driven by multiplicative space-time white noise. We established local well-posedness for the system, proving that for $ \mathcal{F}_0 $-measurable initial data $ \left(\phi_0, \varphi_0\right) $ in the Sobolev space $ H^s(\mathbb{R}) \times H^s(\mathbb{R}) $ with $ s > -5 / 8 $, and with the noise operator $ \Xi $ belonging to the intersection of Hilbert-Schmidt spaces $ L_2^{0, s} \cap L_2^{0, s, -\frac{3}{8}} $, there exists a unique local solution. Furthermore, we demonstrated global well-posedness in the energy space $ L^2(\mathbb{R}) \times L^2(\mathbb{R}) $ for $ L^2 $-valued initial data and with $ \Xi \in L_2^{0, 0} \cap L_2^{0, 0, -\frac{3}{8}} $. The analysis employed Fourier restriction norm methods, utilizing Bourgain-type spaces $ X^{s, b} $ and $ Y^{s_1, s_2, b} $. Key to the proofs was the establishment of crucial linear and bilinear estimates within these spaces and a detailed analysis of the stochastic convolution via Itô calculus. A fixed-point argument was then applied to obtain the local solution, while global existence followed from an invariance property (conservation) of the $ L^2 $ norm, a martingale inequality, and an approximation procedure. The work extends previous results on single stochastic KdV equations to a more complex coupled system, providing a robust framework for analyzing nonlinear wave propagation subject to random perturbations, with applications in plasma physics and fluid dynamics.