Analysis of fractional-order nonlinear dynamic systems under Caputo differential operator

Abstract

The current study presents a detailed analysis of two crucial real-world problems under the Caputo fractional derivative in order to deliver some desired results for the ecosystem. In view of the fact that memory effect plays a vital role in the application, we utilize an advantageous non-local fractional operator to investigate and analyze a mathematical model of the planktonic ecosystem and biological system for the ecosystem on Planet GLIA-2. On the other hand, theoretical and numerical results are given for the model created for phytoplankton, which is of great importance in preventing global warming, and the biological model. Existence and uniqueness are discussed for the solutions of both models with the help of the fixed-point theorem under the Caputo operator. Additionally, the first-order convergent numerical technique which is accurate, conditionally stable, and convergent in obtaining the solution of fractional-order nonlinear systems of ordinary differential equations is utilized to simulate the two governing models. Numerical simulations including different values of arbitrary order rho indicate the righteousness of the conditions for phytoplankton, Jancor, Murrot, and Vekton populations to develop.