Solvability for a couple system of nonlinear fractional differential equations in a Banach space

作者：Liang, Jitai^*; Liu, Zhenhai; Wang, Xuhuan

来源：Fractional Calculus and Applied Analysis, 2013, 16(1): 51-63.

DOI：10.2478/s13540-013-0004-0

• Caputo fractional derivative
• nonlinear fractional differential equations
• measures of noncompactness

In this paper, we study boundary value problems of nonlinear fractional differential equations in a Banach Space E of the following form: {D-0(p)+x(t) = f(1)(t,x(t),y(t)), t is an element of J = [0, 1], D-0(q)+y(t) = f(2)(t,x(t),y(t)), t is an element of J = [0, 1], x(0) + lambda(1)x(1) = g(1)(x,y), y(0) + lambda(2)y(1) = g(2)(x,y), where D0+ denotes the Caputo fractional derivative, 0 < p, q <= 1. Some new results on the solutions are obtained, by the concept of measures of noncompactness and the fixed point theorem of Monch type.

• 单位
  广西民族大学; 保山学院; 云南师范大学