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.


34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
26A33 Fractional derivatives and integrals
34A45 Theoretical approximation of solutions to ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations


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