An operational matrix method for nonlinear variable-order time fractional reaction–diffusion equation involving Mittag-Leffler kernel

Abstract

This paper is concerned with an operational matrix (OM) scheme based on the shifted Chebyshev cardinal functions (SCCFs) of the second kind for numerical solution of the variable-order time fractional nonlinear reaction–diffusion equation. The fractional derivative operator is defined in the sense of Atangana–Baleanu–Caputo. Through the way, a new OM of variable-order fractional derivative is derived for the mentioned cardinal functions. More precisely, the unknown solution is expanded by the SCCFs with undetermined coefficients. Then the expansion substituted in the equation and the generated OM is utilized to extract some algebraic equations. The precision of the established approach is examined through various types of test examples. Numerical simulations confirm the suggested approach is highly accurate to provide satisfactory results.