A numerical method based on the hat functions to solve a category of nonlinear fractional integro-differential equations involving Caputo-Hadamard derivative

In this paper, the Caputo-Hadamard fractional derivative is considered to create a category of fractional integro-differential equations. The hat functions, as a suitable class of basis functions, are used to create a numerical method to solve these equations. To establish this approach, an operational matrix for the Hadamard fractional integral of the hat functions is obtained. The proposed method converts solving the problem under study into solving an algebraic system of nonlinear equations by employing the classical and fractional integral matrices of the hat functions. The convergence of the established method is examined both theoretically and numerically. The accuracy and validity of the developed scheme are examined by solving some numerical examples.