Existence of mild solutions for fractional integrodifferential equations of Sobolev type with nonlocal conditions. (English) Zbl 1242.45009
This paper is concerned with fractional integrodifferential equations of Sobolev type with nonlocal conditions in a separable Banach space. With the help of the theory of propagation families as well as the theory of measures of noncompactness and condensing maps, the authors obtain an existence result of mild solutions for the above equations. Moreover, they present two examples to show applications of the above result.
Fractional integrodifferential equations of Sobolev type appear in the theory of control of dynamical systems, when the controlled system or/and the controller is described by a fractional integrodifferential equation of Sobolev type. Furthermore, the mathematical modeling and simulations of systems and processes are based on the description of their properties in terms of fractional integrodifferential equations of Sobolev type. These new models are more adequate than previously used integer order models, so fractional order integrodifferential equations of Sobolev type have been investigated by many researchers.
Fractional integrodifferential equations of Sobolev type appear in the theory of control of dynamical systems, when the controlled system or/and the controller is described by a fractional integrodifferential equation of Sobolev type. Furthermore, the mathematical modeling and simulations of systems and processes are based on the description of their properties in terms of fractional integrodifferential equations of Sobolev type. These new models are more adequate than previously used integer order models, so fractional order integrodifferential equations of Sobolev type have been investigated by many researchers.
Reviewer: Kun Soo Chang (Seoul)
MSC:
| 45J05 | Integro-ordinary differential equations |
| 45G10 | Other nonlinear integral equations |
| 26A33 | Fractional derivatives and integrals |
| 45N05 | Abstract integral equations, integral equations in abstract spaces |
| 47H08 | Measures of noncompactness and condensing mappings, \(K\)-set contractions, etc. |
| 93C23 | Control/observation systems governed by functional-differential equations |
| 93B05 | Controllability |
Keywords:
Sobolev type; fractional integrodifferential equation; mild solution; nonlocal condition; propagation family; measure of noncompactness; Banach spaceReferences:
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