Numerical analysis of the fractal-fractional diffusion model of ignition in the combustion process

Abstract

The study employs the fractal-fractional operator to derive a distinct variant of the fractal-fractional diffusion equation. To address this challenge, a novel operational matrix technique (OM) is introduced, utilizing shifted Chebyshev cardinal functions (CCFs). Additionally, fundamental functions are employed to establish an OM tailored to the specific derivative in question. Through the application of these operational matrix techniques, the core equation is transformed into an algebraic system, paving the way for the resolution of the presented issue. The study showcases graphical representations of both exact and approximated solutions, accompanied by corresponding error graphs. Furthermore, comprehensive tables present the values of solutions and errors across various examples. For each test case, a comparative analysis of solutions at specific time points is also presented.