Saud Fahad Aldosary

In this paper, we study a nonlinear system of sequential Caputo fractional differential equations equipped with coupled mixed multi-point boundary conditions. In particular, the boundary conditions involve the values of the unknown functions at the endpoints expressed as linear combinations of their values at several interior points, forming a closed system of relations. The existence of solutions is established by applying the Leray–Schauder alternative, while uniqueness is proved using Banach’s contraction principle. In addition, we investigate the Hyers–Ulam stability of the proposed system. Several examples are included to demonstrate the applicability of the theoretical results. Some special cases of the general problem are also discussed.

This study presents a stochastic SVIR epidemic model in which disease transmission rates fluctuate randomly over time, driven by independent, mean-reverting processes with multiplicative noise. These dynamics capture environmental variability and behavioral changes affecting disease spread. We derive analytical expressions for the conditional moments of the transmission rates and establish the existence of their stationary distributions under broad conditions. By averaging over these distributions, we define a stationary effective reproduction number that enables a probabilistic classification of outbreak scenarios. Specifically, we estimate the likelihood of disease persistence or extinction based on transmission uncertainty. Sensitivity analyses reveal that the shape and intensity of transmission variability play a decisive role in epidemic outcomes. Monte Carlo simulations validate our theoretical findings, showing strong agreement between empirical distributions and theoretical predictions. Our results underscore how randomness in disease transmission can fundamentally alter epidemic trajectories, offering a robust mathematical framework for risk assessment under uncertainty.

This paper aims to extend the applications of the projected fractional improved Adomian Decomposition method (fIADM) to the fractional order new coupled Korteweg-de Vries (cKdV) system. This technique is significantly recognized for its effectiveness in addressing nonlinearities and iteratively handling fractional derivatives. The approximate solutions of the fractional-order new cKdV system are obtained by employing the improved ADM in fractional form. These solutions play a crucial role in designing and optimizing systems in engineering applications where accurate modeling of wave phenomena is essential, including fluid dynamics, plasma physics, nonlinear optics, and other mathematical physics domains. The fractional order new cKdV system, integrating fractional calculus, enhances accuracy in modeling wave interactions compared to the classical cKdV system. Comparison with exact solutions demonstrates the high accuracy and ease of application of the projected method. This proposed technique proves influential in resolving fractional coupled systems encountered in various fields, including engineering and physics. Numerical results obtained using Mathematica software further verify and demonstrate its efficacy.

We formulate an iterative approach employing the inertial technique to approximate the anticipated solution for a generalized mixed variational-like inequality, as well as variational inequality and fixed point problems associated with a relatively nonexpansive multivalued mapping within the context of a real Banach space. Additionally, we delve into the robust convergence of our suggested algorithm. Furthermore, we highlight certain implications and present numerical observations to underscore the significance of our findings. The proposed theorem extends and consolidates several previously published works.

In this article, we present some results on fixed points employing relational Geraghty contractions in the setting of metric space endued with a class of transitive binary relations. Our results complement, sharpen and improve several fixed point results of literature. By means of our findings, we discuss an existence and uniqueness theorem regarding the positive solutions of certain boundary value problems associated with a singular fractional differential equations.