Generalized Fractional Differential Equations

Abstract

In this chapter, the theory of linear and nonlinear fractional differential equations is developed and extended to a large class of generalized fractional evolutions. The used method is mostly that of semigroups and propagators as developed in Chapters 4 and 5. As previously, general facts are illustrated on concrete examples. The generalized fractional calculus is usually developed by extending fractional integrals to integral operators with arbitrary integral kernels (or some of their subclasses dictated by the classes of special functions under investigation) and then defining fractional derivatives as the derivatives of these integral operators.