Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 265, Issue 2, Pages 229-248Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1006/jmaa.2000.7194
Keywords
differential equations; fractional order; numerical methods
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We discuss existence, uniqueness, and structural stability of solutions of nonlinear differential equations of fractional order. The differential operators are taken in the Riemann-Liouville sense and the initial conditions are specified according to Caputo's suggestion, thus allowing for interpretation in a physically meaningful way. We investigate in particular the dependence of the solution on the order of the differential equation and on the initial condition, and we relate our results to the selection of appropriate numerical schemes for the solution of fractional differential equations. (C) 2002 Elsevier Science.
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