Application of Topological Degree Method for Solutions of Coupled Systems of Multipoints Boundary Value Problems of Fractional Order Hybrid Differential Equations

作者：Iqbal, Muhammad; Li, Yongjin^*; Shah, Kamal; Khan, Rahmat Ali

来源：Complexity, 2017, 2017: 7676814.

DOI：10.1155/2017/7676814

We established the theory to coupled systems of multipoints boundary value problems of fractional order hybrid differential equations with nonlinear perturbations of second type involving Caputo fractional derivative. The proposed problem is as follows: D-c(alpha)[x(t) = f(t, x(t))] = g(t, y(t), I(alpha)y(t)), t epsilon J = [0, 1], D-c(alpha)[y(t) = f(t, y(t))] = g(t, x(t), I(alpha)x(t)), t epsilon J = [0, 1], (c)D(p)x(0) = Psi(x(eta(1))), x'(0) = 0, ... , x(n2)(0) = 0, (c)D(p)x(1) = Psi(x(eta(2))), (c)D(p)y(0) = Psi(x(eta(1))), y'(0) = 0, ... , y(n2)(0) = 0, (c)D(p)y(1) = Psi(x(eta(2))), where p, eta(1), eta(2) epsilon (0, 1), Psi is linear, D-c(alpha) is Caputo fractional derivative of order alpha, with n = 1 < alpha <= n, n epsilon N, and I-alpha is fractional integral of order alpha. The nonlinear functions f, g are continuous. For obtaining sufficient conditions on existence and uniqueness of positive solutions to the above system, we used the technique of topological degree theory. Finally, we illustrated the main results by a concrete example.

• 出版日期2017
• 单位中山大学