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Zbl 1014.34003
Diethelm, Kai; Ford, Neville J.
Analysis of fractional differential equations. (English)
[J] J. Math. Anal. Appl. 265, No.2, 229-248 (2002). ISSN 0022-247X

The authors discuss the existence, uniqueness and structural stability of solutions to nonlinear differential equations of fractional order. They take the differential operators in the Riemann-Liouville sense and the initial conditions are specified according to Caputo's suggestion, in order to allow for an interpretation in a physically meaningful way.\par They also investigate the dependence of the solution on the order of the differential equation and on the initial condition, and they relate their results to the selection of an appropriate numerical scheme for solving fractional differential equations.
[Ismail Taqi Ali (Safat)]

MSC 2000:: *34A25 Analytical theory of ODE
26A33 Fractional derivatives and integrals (real functions)
34A45 Theoretical approximation of solutions of ODE
65L05 Initial value problems for ODE (numerical methods)

Keywords: differential equations; fractional order; numerical methods; existence; uniqueness; structural stability; solutions

Cited in: Zbl 1118.65079

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