Abstract
We deal with three important aspects of a generalized impulsive fractional order differential equation (DE) involving a nonlinear p-Laplacian operator: the existence of a solution, the uniqueness and the Hyers-Ulam stability. Our problem involves Caputo's fractional derivative. For these goals, we establish an equivalent fractional integral form of the problem and use a topological degree approach for the existence and uniqueness of the solution (EUS). Next, we check the stability of the suggested problem and then demonstrate the results via an illustrative example. In the literature, we could not find articles on the Hyers-Ulam stability of the impulsive fractional order DEs with phi p operator.