Title: Fractional pseudo-Newton method and its use in the solution of a non-linear system that allows the construction of a hybrid solar receiver

Abstract: The following document presents one novel numerical method valid for one and several variables, which using the fractional derivative, allows us to find solutions for some nonlinear systems in the complex space using real initial conditions. This method has at most an order of convergence (at least) linear, but it is easy to implement and it is not necessary to invert some matrix for solving nonlinear systems and linear systems. A non-linear system of equations is presented, which is obtained by studying the possibility of building a hybrid solar receiver, and its stability is briefly analyzed, as well as where a possible solution is found and finally it is solved using the fractional pseudo-Newton method.