Applications of Radial Basis Function Schemes to Fractional Partial Differential Equations

In modeling using diffusion equations, the relationship between fractal geometry and fractional calculus arises by modeling the conditions of the medium as a fractal whose fractional dimension determines the order of this equation. For this reason, it is very useful to have numerical methods that solve them and discretization of the domain is not determinant for the efficiency of the algorithm. In this work, it is proposed to show that meshless methods, in particular methods with radial basis functions (RBF), are an alternative to schemes in differences or structured meshes. We show that we can obtain numerical solutions to some fractional partial differential equations using collocation and RBF, over non equally distributed data.