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

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.