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Nonlinear sequential fractional differential equations in partially ordered spaces. (English) Zbl 1513.34021

Summary: In this paper, some new partially ordered Banach spaces are introduced. Based on those new partially ordered Banach spaces and applying some fixed point theorems, we present a new approach to the theory of nonlinear sequential fractional differential equations. An example illustrating our approach is also discussed.

MSC:

34A08 Fractional ordinary differential equations
34G20 Nonlinear differential equations in abstract spaces
47N20 Applications of operator theory to differential and integral equations
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