Nonuniqueness of solution for initial value problems of impulsive Hilfer fractional differential equations

This paper is mainly concerned with the initial value problem (IVP) for two types of impulsive fractional differential equations (IFrDE) with the Hilfer-generalized fractional derivative. For these IVPs of IFrDE, their equivalent integral equations with an arbitrary constant are built by constructing an approximate solution and calculating the error between the approximate solution and the exact solution, which uncover that there are many solutions for these IVPs of IFrDE. We offer some numerical examples to explain the obtained results.

Automated summary

This paper focuses on the initial value problem for two types of impulsive fractional differential equations with the Hilfer-generalized fractional derivative. By constructing an approximate solution and calculating the error, it is revealed that there are multiple solutions for these equations. Numerical examples are provided to illustrate the obtained results.