Xiufeng GUO

Existence of unique solution to switched fractional differential equations with p-Laplacian operator

ISSN: 1300-0098
Yayın Aralığı: 6
Yayıncı: TÜBİTAK

In this paper, we study a class of nonlinear switched systems of fractional order with p-Laplacian operator. By applying a fixed point theorem for a concave operator on a cone, we obtain the existence and uniqueness of a positive solution for an integral boundary value problem with switched nonlinearity under some suitable assumptions. An illustrative example is included to show that the obtained results are effective.

PDF

___

Agrachev AA, Liberzon D. Lie-algebraic stability criteria for switched systems. SIAM J Control Optim 2001; 40: 253269.
Chai G. Positive solutions for boundary value problem for fractional differential equation with p-Laplacian operator. Bound Value Probl 2012, 2012: 118.
Chen T, Liu W. An anti-periodic boundary value problem for the fractional differential equation with a p-Laplacian operator. Appl Math Lett 2012; 25: 16711675.
Chen T, Liu W, Hu ZG. A boundary value problem for fractional differential equation with p-Laplacian operator at resonance. Nonlinear Anal 2012; 75: 32103217.
Cheng D, Guo L, Lin Y, Wang Y. Stabilization of switched linear systems. IEEE T Automat Contr 2005; 50: 661666.
Cheng D, Wang J, Hu X. An extension of LaSalles invariance principle and its application to multi-agent consensus. IEEE T Automat Contr 2007; 53: 17651770.
Guo D, Lakshmikantham V. Nonlinear Problems in Abstract Cones. New York, NY, USA: Academic Press, 1988.
Gurvits L, Shorten R, Mason O. On the stability of switched positive linear systems. IEEE T Automat Contr 2007; 52: 10991103.