Analysis of multipoint impulsive problem of fractional-order differential equations

Abstract

Abstract This manuscript is related to establishing appropriate results for the existence and uniqueness of solutions to a class of nonlinear impulsive implicit fractional-order differential equations (FODEs). It is remarkable that impulsive differential equations have attracted great popularity due to various important applications in the mathematical modeling of real-world phenomena/processes, particularly in biological or biomedical engineering domains as well as in control theory. The mentioned problem is considered under four-point nonlocal boundary conditions and the derivative is taken in the Caputo sense. Our results are based on fixed-point theorems due to Banach and Schaefer. To justify our results, two suitable examples are given.

Keywords

• Existence and uniqueness
• Nonlocal boundary conditions
• Impulsive-implicit differential equations