Initial value problems for fractional differential equations involving Riemann-Liouville sequential fractional derivative. (English) Zbl 1191.34008
Summary: We discuss the properties of the well-known Mittag-Leffler function, and consider the existence and uniqueness of solution of the initial value problem for fractional differential equation involving Riemann-Liouville sequential fractional derivative by using monotone iterative method.
MSC:
| 34A08 | Fractional ordinary differential equations |
| 34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |
| 34A45 | Theoretical approximation of solutions to ordinary differential equations |
Keywords:
initial value problem; fractional differential equation; Riemann-Liouville sequential fractional derivatives; upper solution and lower solutionReferences:
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