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On recent developments in the theory of abstract differential equations with fractional derivatives

Authors
Journal
Nonlinear Analysis Theory Methods & Applications
0362-546X
Publisher
Elsevier
Publication Date
Volume
73
Issue
10
Identifiers
DOI: 10.1016/j.na.2010.07.035
Keywords
  • Fractional Derivatives
  • Abstract Cauchy Problem
  • Operator Resolvent
  • Abstract Integro-Differential Equations
Disciplines
  • Mathematics

Abstract

Abstract This note is motivated from some recent papers treating the problem of the existence of a solution for abstract differential equations with fractional derivatives. We show that the existence results in [Agarwal et al. (2009) [1], Belmekki and Benchohra (2010) [2], Darwish et al. (2009) [3], Hu et al. (2009) [4], Mophou and N’Guérékata (2009) [6,7], Mophou (2010) [8,9], Muslim (2009) [10], Pandey et al. (2009) [11], Rashid and El-Qaderi (2009) [12] and Tai and Wang (2009) [13]] are incorrect since the considered variation of constant formulas is not appropriate. In this note, we also consider a different approach to treat a general class of abstract fractional differential equations.

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