Positive solutions for an impulsive boundary value problem with Caputo fractional derivative

Abstract

In this work we use fixed point theorem method to discuss the existence of positive solutions for the impulsive boundary value problem with Caputo fractional derivative

Existence of Solutions for a Periodic Boundary ValueProblem with Impulse and Fractional Derivative Dependence

“…In this paper, we first give an equivalent integral form of solutions for problem (1) using some new Green's functions. Next, we present some sufficient conditions for the existence of solutions for problem (1), where the nonlinear and impulse terms satisfy some nonlinear and linear growth conditions, which are different from the conditions in [36][37][38]. Finally, we present three examples to illustrate our main results.…”

“…and some sufficient conditions on the existence and uniqueness of solutions for problem (2) are obtained under Lipschitz conditions. In [38], Zhang and Xu studied the following impulsive periodic boundary value problem with the Caputo fractional derivative:…”