Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 235, pp. 1-10.

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

Authors:  Khaled M. Furati    (King Fahd Univ., Dhahran, Saudi Arabia)
          Mohammed D. Kassim  (King Fahd Univ., Dhahran, Saudi Arabia)
          Nasser-eddine Tatar (King Fahd Univ., Dhahran, Saudi Arabia)

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.

Submitted September 3, 2013. Published October 22, 2013.
Math Subject Classifications: 26D10, 42B20, 26A33, 35J05, 35J25.
Key Words: Cauchy problem; critical exponent;
           fractional differential inequality; 
           Hilfer fractional derivative; test function method.