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2 2010

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Nonlocal impulsive problems for fractional differential equations with time-varying generating operators in Banach spaces

Wang J., Yang Y., Wei W.

Opuscula Mathematica

2010

Vol. 30, no. 3

361-381

In this paper, we study the existence and uniqueness of the PC-mild solution for a class of impulsive fractional differential equations with time-varying generating operators and nonlocal conditions. By means of the generalized Ascoli-Arzela Theorem given by us and the fixed point theorem, some existence and uniqueness results are obtained. Finally, an example is given to illustrate the theory.

Fractional nonlocal integrodifferential equations of mixed type with time-varying generating operators and optimal control

Wang J., Wei W., Yang Y.

Opuscula Mathematica

2010

Vol. 30, no. 2

217-234

In this paper, a class of fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is considered. Using a contraction mapping principle and Krasnoselskii's fixed point theorem via Gronwall's inequailty, the existence and uniqueness of mild solution are given. The existence of optimal pairs of systems governed by fractional integrodifferential equations of mixed type with time-varying generating operators and nonlocal conditions is also presented.