Existence and uniqueness theorem for a class of delay differential equations with left and right Caputo fractional derivatives. (English) Zbl 1152.81550

Maraaba, Thabet; Baleanu, Dumitru; Jarad, Fahd

J. Math. Phys. 49, No. 8, 083507, 11 p. (2008).

Authors’ summary: The existence and uniqueness theorems for functional right-left delay and left-right advanced fractional functional differential equations with bounded delay and advance, respectively, are proved. The continuity with respect to the initial function for these equations is also proved under some Lipschitz kind conditions. The Q-operator is used to transform the delay-type equation to an advanced one and vice versa. An example is given to clarify the results.

MSC:

34A12	Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
26A33	Fractional derivatives and integrals
34K05	General theory of functional-differential equations

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