A Hilbert Space Approach to Fractional Differential Equations
Keyword(s):
AbstractWe study fractional differential equations of Riemann–Liouville and Caputo type in Hilbert spaces. Using exponentially weighted spaces of functions defined on $${\mathbb {R}}$$ R , we define fractional operators by means of a functional calculus using the Fourier transform. Main tools are extrapolation- and interpolation spaces. Main results are the existence and uniqueness of solutions and the causality of solution operators for non-linear fractional differential equations.
2019 ◽
Vol 3
(1)
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pp. 46-52
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2010 ◽
Vol 2010
(1)
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pp. 364560
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2012 ◽
Vol 64
(10)
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pp. 3310-3320
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2011 ◽
Vol 31
(6)
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pp. 2122-2130
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