Fractional differential equations and initial value problems. (English) Zbl 0919.34005

Davison, Matt; Essex, Christopher

Math. Sci. 23, No. 2, 108-116 (1998).

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:

34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A33	Fractional derivatives and integrals

Keywords:

anomalous diffusion; fractional differentiation; initial values; fractional differential operator; Riemann-Liouville fractional integral