A Class of Fractional-Order Quadratic Isothermal Auto-Catalytic Chemical Systems

In this study, we investigate the fractional-order formulations of the quadratic isothermal autocatalytic chemical system (FQIACS) and analyze their corresponding numerical solutions. Two non-singular fractional operators are considered, namely the Liouville–Caputo and Caputo–Fabrizio derivatives. The governing fractional models are transformed into an algebraic system using a combination of the nonstandard finite difference scheme and the spectral collocation method based on Shifted Vieta–Lucas orthogonal polynomials. The resulting nonlinear algebraic systems are solved using the Newton–Raphson method. Since closed-form analytical solutions are generally unavailable for noninteger orders, the accuracy of the proposed numerical approximations is evaluated through the residual error function. The results demonstrate the effectiveness and reliability of the developed numerical framework for handling fractional chemical kinetics involving different memory kernels.