A Hilbert Space Approach to Fractional Differential Equations

Abstract We study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces functions defined on $${\mathbb {R}}$$ R , we define operators by means a functional calculus using the Fourier transform. Main tools are extrapolation- interpolation results existence uniqueness solutions causality solution for non-linear equations.