Monotone iterative technique for \(S\)-asymptotically periodic problem of fractional evolution equation with finite delay in ordered Banach space. (English) Zbl 1471.34143
In this article, authors consider a fractional evolution equation with delay in ordered Banach space. The fractional derivative is taken in the sense of Caputo. The main aim is to establish the existence of S-asymptotically periodic solution. The main technique used is the concept of monotone iteration. This technique of upper and lower solution is a quite powerful method to obtain the solution. It also provides an iterative method for the solution. The monotone sequences of the lower and upper approximate solutions converge to the minimal and maximal solutions between the lower and upper solutions. The existence of minimal and maximal solutions have been shown by the authors. At the end, examples are also given for illustration.
Reviewer: Syed Abbas (Mandi)
MSC:
| 34K30 | Functional-differential equations in abstract spaces |
| 34K37 | Functional-differential equations with fractional derivatives |
| 34K07 | Theoretical approximation of solutions to functional-differential equations |
| 34K13 | Periodic solutions to functional-differential equations |
| 47H07 | Monotone and positive operators on ordered Banach spaces or other ordered topological vector spaces |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
Keywords:
\(S\)-asymptotically periodic mild solutions; fractional evolution equation; monotone iterative technique; positive \(C_0\)-semigroup; measure of noncompactness; finite delayReferences:
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