Numerical solution of variable order fractional nonlinear quadratic integro-differential equations based on the sixth-kind Chebyshev collocation method

Abstract

In this paper, a sixth-kind Chebyshev collocation method will be considered for solving a class of variable order fractional nonlinear quadratic integro-differential equations (V-OFNQIDEs). The operational matrix of variable order fractional derivative for sixth-kind Chebyshev polynomials is derived and then, a collocation approach is employed to reduce the V-OFNQIDE to a system of nonlinear algebraic equations. Convergence analysis of the proposed method is evaluated and the rate of convergence is established. Finally, some numerical test examples are investigated to validate the accuracy and robustness of the proposed approach.