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Existence and uniqueness of solutions for the Cauchy-type problems of fractional differential equations. (English) Zbl 1197.34004
The authors are concerned with presenting existence and uniqueness results for Cauchy-type problems for fractional differential equations based on the Riemann-Liouville or Hadamard fractional derivative. The authors present a sequence of lemmas providing basic theory and draw attention to new features in their work that highlight differences from the published results in the monograph by A. A. Kilbas, H. M. Srivastava and J. J. Trujillo [Theory and applications of fractional differential equations. Amsterdam: Elsevier (2006; Zbl 1092.45003)]. Examples are presented that highlight these differences in the theoretical results.
MSC:
34A08Fractional differential equations
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions