Numerical study on fractional order nonlinear SIR-SI model for dengue fever epidemics.

This paper focuses on a combined SIR-SI epidemic model to evaluate the transmission dynamics of dengue fever, integrating the susceptible-infected-recovered (SIR) framework for the human population with the susceptible-infected (SI) framework for mosquitoes. The model is formulated as a system of nonlinear differential equations and is further extended by incorporating fractional-order derivatives in the Caputo sense to capture memory effects in disease transmission. A thorough investigation of the disease-free and endemic equilibrium points is conducted, encompassing both local and global stability at the disease-free state.

Numerical pricing of European options under time-fractional Black-Scholes equation in financial markets.

The time-fractional Black-Scholes model (TFBSM) incorporating a Caputo derivative operator is developed to analyze price dynamics in fractal market systems with correlated fluctuations. This paper focuses on developing a numerical approach to derive an approximate solution for the TFBSM of order 0<α<1 in problems related to European options using the Legendre collocation technique. The primary advantage of this method is that the function is approximated with shifted Legendre polynomials in both space and time directions, using fewer nodal points for improved results.

Effect of heat transfer on hybrid nanofluid flow in converging/diverging channel using fuzzy volume fraction.

This work explores the magneto-hydrodynamics (MHD) Jeffery-Hamel nanofluid flow between two rigid non-parallel plane walls with heat transfer by employing hybrid nanoparticles, especially Cu and Cu-Al[Formula: see text]O[Formula: see text]. Here the MHD nanofluid flow problem is extended with fuzzy volume fraction and heat transfer with diverse nanoparticles to cover the influence of thermal profiles with hybrid nanoparticles on the fuzzy velocity profiles. The nanoparticle volume fraction is described with a triangular fuzzy number ranging from 0 to [Formula: see text].

Study on generalized fuzzy fractional human liver model with Atangana-Baleanu-Caputo fractional derivative.

This study aims to develop a novel fuzzy fractional model for the human liver that incorporates the ABC fractional differentiability, also known as ABC gH-differentiability, based on the generalized Hukuhara derivative. In addition, a novel fuzzy double parametric -homotopy analysis method with a generalized transform and ABC gH-differentiability is used to deal with the fuzzy mathematical model and examine its convergence analysis. The stability of the unique equilibrium point for the fuzzy fractional human liver model and the existence of a unique solution in the proposed model are investigated using the Arzela-Ascoli theorem and Schauder's fixed-point theory.