A note on the fractional Cauchy problems with nonlocal initial conditions

“…The following lemma follows from the results in [16][17][18][19][20] and will be used throughout this paper. [21]) The operatorsS q (t) andT q (t) have the following properties:…”

Section: Definition 23 the Caputo Derivative Of Ordermentioning

confidence: 99%

Stochastic fractional perturbed control systems with fractional Brownian motion and Sobolev stochastic non local conditions

2017

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This paper investigates the approximate controllability for Sobolev type stochastic perturbed control systems of fractional order with fractional Brownian motion and Sobolev fractional stochastic nonlocal conditions in a Hilbert space, A new set of sufficient conditions are established by using semigroup theory, fractional calculus, stochastic integrals for fractional Brownian motion, Banach's fixed point theorem. The results are obtained under the assumption that the associated linear system is approximately controllable. Finally, an example is also given to illustrate the obtained theory.

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“…The problem (Q) has been extended to various kinds of differential equations and differential inclusions. We refer the readers to and the references cited there for more information in this direction.…”

Section: Introductionmentioning

confidence: 99%

“…The problem (Q) has been extended to various kinds of differential equations and differential inclusions. We refer the readers to [13][14][15][16][17][18][19][20][21][22][23] and the references cited there for more information in this direction. Of interest is the case that A generates a compact C 0 -semigroup .T.t// t 0 .…”

Section: Introductionmentioning

confidence: 99%