Fractional Sobolev-type inequalities

Abstract

Here we present univariate Sobolev-type fractional inequalities involving fractional derivatives of Canavati, Riemann–Liouville and Caputo types. The results are general L _p inequalities forward and converse on a closed interval. We give an application to a fractional ODE. We present also the mean Sobolev-type fractional inequalities.

Keywords:

• Sobolev-type inequality
• fractional inequality
• fractional derivative

AMS Subject Classifications:

• 26A33
• 26D10
• 26D15