On a Periodic Boundary Value Problem for Fractional Quasilinear Differential Equations with a Self-Adjoint Positive Operator in Hilbert Spaces
Keyword(s):
In this paper we study the existence of a mild solution of a periodic boundary value problem for fractional quasilinear differential equations in a Hilbert spaces. We assume that a linear part in equations is a self-adjoint positive operator with dense domain in Hilbert space and a nonlinear part is a map obeying Carathéodory type conditions. We find the mild solution of this problem in the form of a series in a Hilbert space. In the space of continuous functions, we construct the corresponding resolving operator, and for it, by using Schauder theorem, we prove the existence of a fixed point. At the end of the paper, we give an example for a boundary value problem for a diffusion type equation.
2007 ◽
Vol 193
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pp. 560-571
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1996 ◽
Vol 204
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pp. 65-73
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2002 ◽
Vol 138
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pp. 205-217
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2004 ◽
Vol 155
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pp. 709-726
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2011 ◽
Vol 47
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pp. 1426-1434
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