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Search Results: 1 - 10 of 11986 matches for " Sung Koo Kang "
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 Abstract and Applied Analysis , 2014, DOI: 10.1155/2014/631419 Abstract: We introduce the notion of h-stability for fractional differential systems. Then we investigate the boundedness and h-stability of solutions of Caputo fractional differential systems by using fractional comparison principle and fractional Lyapunov direct method. Furthermore, we give examples to illustrate our results. 1. Introductions and Preliminaries Lakshmikantham et al. [1–5] investigated the basic theory of initial value problems for fractional differential equations involving Riemann-Liouville differential operators of order . They followed the classical approach of the theory of differential equations of integer order in order to compare and contrast the differences as well as the intricacies that might result in development [6, Vol. I]. Li et al. [7] obtained some results about stability of solutions for fractional-order dynamic systems using fractional Lyapunov direct method and fractional comparison principle. Choi and Koo [8] improved on the monotone property of Lemma？？ in [5] for the case with a nonnegative real number . Choi et al. [9] also investigated Mittag-Leffler stability of solutions of fractional differential equations by using the fractional comparison principle. In this paper we introduce the notion of -stability for fractional differential equations. Then, we investigate the boundedness and -stability of solutions of Caputo fractional differential systems by using fractional comparison principle and fractional Lyapunov direct method. Furthermore, we give some examples to illustrate our results. For the basic notions and theorems about fractional calculus, we mainly refer to some books [5, 10, 11]. We recall the notions of Mittag-Leffler functions which were originally introduced by Mittag-Leffler in 1903 [12]. Similar to the exponential function frequently used in the solutions of integer-order systems, a function frequently used in the solutions of fractional order systems is the Mittag-Leffler function, defined as where and is the Gamma function [11]. The Mittag-Leffler function with two parameters has the following form: where and . For , we have . Also, . Note that the exponential function possesses the semigroup property (i.e., for all ), but the Mittag-Leffler function does not satisfy the semigroup property unless or [13]. We recall briefly the notions and basic properties about fractional integral operators and fractional derivatives of functions [5, 10]. Let . Definition 1 (see [5]). The Riemann-Liouville fractional integral of order of a function is defined as where (provided that the integral exists in the Lebesgue
 iBusiness (IB) , 2012, DOI: 10.4236/ib.2012.44046 Abstract: This study analyzes the trust level relationships of the warehousing industry firms in the city of Busan, South Korea in regards to their determinants and spatial dimensions. A firm’s environment, such as reputation and renown, forms the relationship between the firm and other firms. The trust levels between firms were determined by the determinants of the trust: Long-term and repeated interaction, information sharing and reciprocity, and interdependence and asset specificity all had an important effect upon the micro or highest level of trust. Proximity and uncertainty influenced the meso or middle level of trust. The culture and norms of the firms & institutional formality affected the macro or lowest level of trust. It was found that the higher the trust levels, the more the respective spatial dimensions generated by the relationship between firms expanded to the national and international dimensions.