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Controllability of nonlinear implicit fractional integrodifferential systems

100%

Balachandran K. , Divya S.

tom 24

nr 4

713-722

In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo's fixed point theorem. Examples are included to verify the result.

On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces

88%

Yang Y. , Wang J.

Opuscula Mathematica

2011

tom Vol. 31, no. 3

443-455

In this paper, we study a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. Existence results of mild solutions are proved for a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. The main results are obtained by using the Schaefer fixed point theorem and semigroup theory. Finally, an example is given for demonstration.

Controllability for some partial functional integrodifferential equations with nonlocal conditions in Banach spaces

88%

Ezzinbi K. , Degla G. , Ndambomve P.

tom 35

nr 1

25-46

This work concerns the study of the controllability of some partial functional integrodifferential equation with nonlocal initial conditions in Banach spaces. It gives sufficient conditions that ensure the controllability of the system by supposing that its linear homogeneous part admits a resolvent operator in the sense of Grimmer, and by making use of the measure of noncompactness and the Mönch fixed-point theorem. As a result, we obtain a generalization of the work of Y.K. Chang, J.J. Nieto and W.S. Li (J. Optim. Theory Appl. 142, 267-273 (2009)), without assuming the compactness of the resolvent operator. An example of application is given for illustration.

A class of nonlocal integrodifferential equations via fractional derivative and its mild solutions

75%

Wang J. , Yan X. , Zhang X. H. , Wang T. M. , Li X. Z.

Opuscula Mathematica

2011

tom Vol. 31, no. 1

119-135

In this paper, we discuss a class of integrodifferential equations with nonlocal conditions via a fractional derivative of the type: [formula]. Some sufficient conditions for the existence of mild solutions for the above system are given. The main tools are the resolvent operators and fixed point theorems due to Banach's fixed point theorem, Krasnoselskii's fixed point theorem and Schaefer's fixed point theorem. At last, an example is given for demonstration.

Controllability of nonlinear implicit fractional integrodifferential systems

63%

Balachandran K. , Divya S.

2014

tom Vol. 24, no. 4

713--722

In this paper, we study the controllability of nonlinear fractional integrodifferential systems with implicit fractional derivative. Sufficient conditions for controllability results are obtained through the notion of the measure of noncompactness of a set and Darbo’s fixed point theorem. Examples are included to verify the result.