A fractional order pyrolysis model with Atangana-Baleanu-Caputo derivative: analysis and numerical simulation

Abstract

Pyrolysis is key to transforming biomass and organic waste into useful energy products. However, standard integer-order models poorly capture the memory and heredity effects that significantly affect the thermal decomposition dynamics of pyrolysis. In this study, we developed a pyrolysis model in the Atangana-Baleanu-Caputo (ABC) sense to more accurately depict the memory-based behavior of biomass decomposition under non-isothermal conditions. The proposed ABC fractional derivative model extends the classical two-stage kinetic model by combining a fractional derivative with a non-local and non-singular kernel, allowing past thermal states to influence the present system dynamics. Theoretical analyses demonstrate the positivity, existence, and uniqueness of solutions as well as Ulam-Hyers (UH) and generalized UH stability. To illustrate the dynamic response of the system, a predictor-corrector method was employed to compute approximate solutions under various fractional orders and heating rates. Numerical studies have shown that smaller fractional orders improve the rate of thermal conversion and maintain controlled temperature levels. These results show that fractional order modeling is a reliable and useful method for studying pyrolysis processes. It could also help with the design and improvement of biomass conversion systems that use less energy.