Chaotic Dynamic Behavior of a Fractional-Order Financial System with Constant Inelastic Demand

Nanofluid, a significant branch of fluid mechanics, plays a pivotal role in thermal management, optics, biomedical engineering, energy harvesting, and other fields. The nanoparticles present in the fluid render the continuum mechanics ineffective, necessitating the adoption of fractional calculus to elucidate the effects of nanoparticles on the motion properties of the nanofluid. This article applies the modified extended tanh-function technique to solve two classical Schrödinger equations, the fractional Phi-4 model and the conformable fractional Boussinesq model, for nanofluids. Multiple exact solutions are obtained, and the corresponding graphical representations are provided to elucidate the basic properties of the nanofluid. This article provides new research perspectives for the development of nanofluids.

Exact solutions of a class of generalized nanofluidic models

Zeng,

Ming,

Jiang

et al. 2024

Fourier spectral method for the fractional-in-space coupled Whitham–Broer–Kaup equations on unbounded domain

Zhao,

Zhang

2024

Due to the nonlocality of fractional derivatives, the numerical methods for solving nonlinear fractional Whitham–Broer–Kaup (WBK) equations are time-consuming and tedious. Therefore, it is a research hotspot to explore the numerical solution of fractional-order WBK equation. The main goal of this study is to provide an efficient method for the fractional-in-space coupled WBK equations on unbounded domain and discover some novel anomalous transmission behaviors. First, the numerical solution is compared with the exact solution to determine the validity of the proposed method on large time-spatial domain. Then, anomalous transmission of waves propagation of the fractional WBK equation is numerically simulated, and the influence of different fractional-order derivatives on wave propagation of the WBK equation is researched. Some novel anomalous transmission behaviors of wave propagation of the fractional WBK equation on unbounded domain are shown.

Innovative analysis to the time-fractional q-deformed tanh-Gordon equation via modified double Laplace transform method

Ali,

Mohamed,

Alharbi

et al. 2024

In this study, we introduce an efficient analysis of a new equation, termed the time-fractional q q -deformed tanh-Gordon equation (TGE), which is the fractional form of the q q -deformed TGE that was recently introduced by Ali and Alharbi. This equation represents a significant advancement in the field of mathematical physics, which is due to its applications in many fields including superconductivity and fiber optics. It has many applications in condensed matter physics and in modeling physical systems that exhibit violated symmetries. We investigate the q q -deformed TGE in fractional form using Caputo fractional derivative to capture non-local and memory effects, which means they can take into account the entire history of a function rather than just its current value. Notably, this equation has not been previously solved in fractional form, making our approach pioneering in its analysis. We solve this equation utilizing the modified double Laplace transform method, which is considered a semi-analytical technique that combines the double Laplace transform with Adomian polynomials to enable us to extract nonlinear terms. This method renowned for its efficacy in handling fractional differential equations; this is evident from the results obtained in the tables by comparing the analytical solution with the approximate solution we obtained, as well as by calculating the absolute error between them. We examine the existence and the uniqueness of the solution utilizing Schaefer’s fixed-point theorem. Different graphs in 2D and 3D are presented to clarify the effect of different parameters on the behavior of the solution, specially the fractional operator and the deformation parameter q q .