Langevin equation involving three fractional orders. (English) Zbl 1436.26006
Existence and uniqueness of initial value problems for the nonlinear Langevin equation involving three fractional orders are the main objects of study of this note. A new norm is employed to this end and the desired results follow by using the Banach contraction mapping principle. The given internal noise depends on the fractional derivatives, described in the Caputo sense. The obtained results are valid, due to avoiding some usual restrictive hypotheses, for classes of functions wider than \(C[0, 1]\).
Reviewer: Sorin-Mihai Grad (Wien)
MSC:
| 26A33 | Fractional derivatives and integrals |
| 34A08 | Fractional ordinary differential equations |
| 47E05 | General theory of ordinary differential operators |
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