Analysis of Fractional Differential Equations in Higher-dimensional Complex System With Proportional Delay, Discrete Term, and Nonlinear Coupling: Applications in a Biological Model and Porous Media
Year: 2026
Type: article
Abstract: This paper considers a general coupled system of [Formula: see text]-equations with the Caputo–Fabrizio derivative. We establish the existence theory for the system using fixed-point analysis. Sufficient conditions are derived to ensure the existence and uniqueness of the solution. Additionally, a real-life example of a two-species household model is demonstrated through our analysis. Furthermore, we present graphical solutions corresponding to various fractional orders by employing an advanced numerical algorithm. Three distinct sets of fractional-order values are used in this context. An additional example of a fractional porous media equation is also provided to demonstrate the proposed method, which can be effectively solved using the outlined approach.
Source: Fractals
Authors: SALMA NOOR, AMAN ULLAH, MUHAMMAD TAYYAB, SALMA HAQUE, NABIL MLAIKI
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7128792760