Existence of Solutions of a New Class of Impulsive Initial Value Problems of Singular Nonlinear Fractional Differential Systems

摘要

Sufficient conditions are given for the existence of solutions of impulsive boundary value problems for singular nonlinear fractional differential systems. We allow the nonlinearities p(t)f(t,y)$$p(t)f(t,y)$$ and q(t)g(t,x)$$q(t)g(t,x)$$ in fractional differential equations to be singular at t=0$$t!=!0$$. Both f$$f$$ and g$$g$$ may be super-linear and sub-linear. The analysis relies on some well-known fixed point theorems. The initial value problem discussed may be seen as a generalization of some ecological models. An example is given to illustrate the efficiency of the main theorems. A conclusion section is given at the end of the paper.