In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By u...In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.展开更多
In this paper, a robust fractional order fuzzy P ＋ fuzzy I ＋ fuzzy D （FOFP ＋ FOFI ＋ FOFD） controller is presented for a nonlinear and uncertain 2-1ink planar rigid manipulator. It is a nonlinear fuzzy controller...In this paper, a robust fractional order fuzzy P ＋ fuzzy I ＋ fuzzy D （FOFP ＋ FOFI ＋ FOFD） controller is presented for a nonlinear and uncertain 2-1ink planar rigid manipulator. It is a nonlinear fuzzy controller with variable gains that makes it self- adjustable or adaptive in nature. The fractional order operators further make it more robust by providing additional degrees of freedom to the design engineer. The integer order counterpart, fuzzy P ＋ fuzzy I ＋ fuzzy D （FP ＋ FI ＋ FD） controller, for a comparative study, was realized by taking the integer value for the fractional order operators in FOFP ＋ FOFI ＋ FOFD controller. The performances of both the fuzzy controllers are evaluated for reference trajectory tracking and disturbance rejection with and without model uncertainty and measurement noise. Genetic algorithm was used to optimize the parameters of controller under study for minimum integral of absolute error. Simulation results demonstrated that FOFP ＋ FOFI ＋ FOFD controller show much better performance as compared to its counterpart FP ＋ FI ＋ FD controller in servo as well as the regulatory problem and in model uncertainty and noisy environment FOFP ＋ FOFI ＋ FOFD controller demonstrated more robust behavior as compared to the FP ＋ FI ＋ FD controller. For the developed controller bounded-input and bounded-output stability conditions are also developed using Small Gain Theorem.展开更多
In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study ...In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.展开更多
基金supported by Natural Science Foundation of China（No.11171220） Support Projects of University of Shanghai for Science and Technology（No.14XPM01）
文摘In this paper,we concern ourselves with the existence of positive solutions for a type of integral boundary value problem of fractional differential equations with the fractional order linear derivative operator. By using the fixed point theorem in cone,the existence of positive solutions for the boundary value problem is obtained. Some examples are also presented to illustrate the application of our main results.
文摘In this paper, a robust fractional order fuzzy P ＋ fuzzy I ＋ fuzzy D （FOFP ＋ FOFI ＋ FOFD） controller is presented for a nonlinear and uncertain 2-1ink planar rigid manipulator. It is a nonlinear fuzzy controller with variable gains that makes it self- adjustable or adaptive in nature. The fractional order operators further make it more robust by providing additional degrees of freedom to the design engineer. The integer order counterpart, fuzzy P ＋ fuzzy I ＋ fuzzy D （FP ＋ FI ＋ FD） controller, for a comparative study, was realized by taking the integer value for the fractional order operators in FOFP ＋ FOFI ＋ FOFD controller. The performances of both the fuzzy controllers are evaluated for reference trajectory tracking and disturbance rejection with and without model uncertainty and measurement noise. Genetic algorithm was used to optimize the parameters of controller under study for minimum integral of absolute error. Simulation results demonstrated that FOFP ＋ FOFI ＋ FOFD controller show much better performance as compared to its counterpart FP ＋ FI ＋ FD controller in servo as well as the regulatory problem and in model uncertainty and noisy environment FOFP ＋ FOFI ＋ FOFD controller demonstrated more robust behavior as compared to the FP ＋ FI ＋ FD controller. For the developed controller bounded-input and bounded-output stability conditions are also developed using Small Gain Theorem.
基金supported by NSF grant DMS-1509505a postdoctoral fellowship of the National Science Foundation(No.DMS-1103786)
文摘In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.
