Numerical Solution of the Multiterm Time‐Fractional Model for Heat Conductivity by Local Meshless Technique

Abstract

Fractional partial differential equation models are frequently used to several physical phenomena. Despite the ability to express many complex phenomena in different disciplines, researchers have found that multiterm time-fractional PDEs improve the modeling accuracy for describing diffusion processes in contrast to the results of a single term. Nowadays, it attracts the attention of the active researchers. The aim of this work is concerned with the approximate numerical solutions of the three-term time-fractional Sobolev model equation using computationally attractive and reliable technique, known as a local meshless method. Because of the meshless character and the simple application in higher dimensions, there is a growing interest in meshless techniques. To assess the reliability and accuracy of the proposed method, three test problems and two types of irregular domains are taken into account.

Global Existence and Fixed-Time Synchronization of a Hyperchaotic Financial System Governed by Semi-Linear Parabolic Partial Differential Equations Equipped with the Homogeneous Neumann Boundary Condition

“…In the meantime, every measure taken to deal with problems in the financial system would necessarily influence the economic development in the future, and therefore, the memory effect that exists in dynamical systems concerning economic evolution should not be neglected. However, as remarked in Reference [8] (see also References [4,9,10]), the memory effect in dynamical systems driven by financial behaviors could result in dissipation. In view of these two phenomena, it seems to be more natural to construct systems of parabolic partial differential equations, whose space variables run over a line segment or a planar region, to track the complex financial behaviors in the real-world markets.…”