Controllability of nonlinear implicit fractional integrodifferential systems
نویسندگان
چکیده
Integrodifferential equations arise in many fields of science and engineering such as fluid dynamics, biological models, and chemical kinetics. A detailed investigation of integrodifferential equations and their solution via the Laplace transform method can be found in the work of Burton (1983). Recently, fractional integrodifferential equations have been used to model various physical phenomena such as heat conduction in materials with memory, combined conduction, convection and radiation problems (Caputo, 1967; Olmstead and Handelsman, 1976; Sabatier et al., 2007), and numerical methods for such equations can be found in the works of Mittal and Nigam (2008) as well as Rawashdeh (2011). Models represented by neutral differential equations are encountered in theoretical epidemiology, physiology and population dynamics. It is interesting to introduce a fractional derivative for these models and study their qualitative behaviors. Controllability is one of the fundamental concepts in control theory and plays a major role in many control problems such as stabilization of unstable systems by feedback or optimal control (Klamka, 1993). This problem can be studied by using different techniques, among which the fixed-point technique is the most powerful method for establishing the controllability results of nonlinear dynamical systems (see Balachandran and Dauer, 1987; Klamka, 1975a; 1975b; 1975c; 1999; 2001; 2008). Dacka (1980) introduced a method based on the measure of non compactness of a set and Darbo’s fixed-point theorem for studying the controllability of nonlinear systems with an implicit derivative. This method was extended to a larger class of dynamical systems by Balachandran (1988).
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عنوان ژورنال:
- Applied Mathematics and Computer Science
دوره 24 شماره
صفحات -
تاریخ انتشار 2014