| The so-called “matrix approach” to discretization of operators of arbitrary real (integer and non-integer) order and to numerical solution of fractional-order differential and integral equations is presented in detail. This method allows easy, uniform, and transparent solution of ordinary fractional differential equations, partial fractional differential equations, and ordinary fractional integral equations. It works for equations with a mixture of left-sided, right-sided, and symmetric fractional-order operators, for equations with derivatives of variable orders, distributed orders, and for equations with delayed fractional-order derivatives. Recent improvements include the extension of this method to non-uniform grids and variable step lengths. The MATLAB toolboxes that implement this method are presented, too, and are used in illustrative examples of numerical solution of various standard types of differential equations of non-integer orders. | |