On a class of fractional order differential inclusions with infinite delays

Abstract

Our aim is to study fractional order differential inclusions with infinite delays in Banach spaces. We impose the regularity condition on multivalued nonlinearity in terms of measures of noncompactness to get the existence result. Some properties of the solution map are proved.

Keywords:

• fractional order differential inclusion
• fractional derivative
• functional differential inclusion
• infinite delay
• initial value problem
• continuous dependence
• multivalued map
• measure of noncompactness
• fixed point
• condensing map

AMS Subject Classifications::

• 34K37
• 26A33
• 34A60
• 34G25
• 34K09
• 34K30
• 47H04
• 47H08
• 47H10
• 47H11

Acknowledgements

The authors would like to express their gratitude to the referee for the helpful comments and suggestions, which resulted in the improvements of the manuscript. The work is partially supported by the Taiwan NSC Grant 98-2923-E-110-003-MY3, 99-2115-M-110-007-MY3 and the Russian FBR-Taiwan NSC Grant 09-01-92003-NNS.