Fixed point theorem combined with variational methods for a class of nonlinear impulsive fractional problems with derivative dependence

Abstract

In this article, we deal with a class of nonlinear impulsive problems of fractional-order in which nonlinearity is due to the fractional-order derivative term. The investigation involved a fixed point theorem with a combination of variational approach and critical point theory to establish sufficient conditions for the existence of at least one solution. First, a damped problem is discussed by using the critical point theory and variational approach, then the solutions of the damped problem and the main problem are connected with the assistance of a fixed point theorem. Towards the end, to illustrate our outcomes, two examples are given.

Keywords

• fixed point theorem
• variational methods
• fractional impulsive boundary value problem
• critical points