Non-existence of global solutions for a differential equation involving Hilfer fractional derivative

Abstract

We consider a basic fractional differential inequality with a fractional derivative named after Hilfer and a polynomial source. A non-existence of global solutions result is proved in an appropriate space and the critical exponent is shown to be optimal.

Keywords

• Cauchy problem
• critical exponent
• fractional differential inequality
• Hilfer fractional derivative
• test function method