On a class of fractional order differential inclusions with infinite delays

Abstract

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 inclusionfractional derivativefunctional differential inclusioninfinite delayinitial value problemcontinuous dependencemultivalued mapmeasure of noncompactnessfixed pointcondensing mapAMS Subject Classifications:: 34K3726A3334A6034G2534K0934K3047H0447H0847H1047H11 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.