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Analysis of fractional differential equations. (English) Zbl 1014.34003
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. 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.

34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
26A33Fractional derivatives and integrals (real functions)
34A45Theoretical approximation of solutions of ODE
65L05Initial value problems for ODE (numerical methods)
Full Text: DOI
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