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Fractional differential equations and initial value problems. (English) Zbl 0919.34005
Summary: An alternative definition of a fractional differential operator corresponding to the Riemann-Liouville fractional integral is introduced. The authors demonstrate that from a naturally-arising selection of possible definitions, the alternative version is the only one suitable for normal initial value problems in the context of fractional calculus, while the standard definition is preferable for certain integral equations.
MSC:
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
26A33Fractional derivatives and integrals (real functions)