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Monotone iterative technique for fractional evolution equations in Banach spaces. (English) Zbl 1226.35084

Summary: We investigate the initial value problem for a class of fractional evolution equations in a Banach space. Under some monotone conditions and noncompactness measure conditions of the nonlinearity, the well-known monotone iterative technique is then extended for fractional evolution equations, which provides computable monotone sequences that converge to the extremal solutions in a sector generated by upper and lower solutions. An example to illustrate the applications of the main results is given.

MSC:

35R11 Fractional partial differential equations
47H07 Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces
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