Numerical approach to the controllability of fractional order impulsive differential equations

Abstract

In this manuscript, a numerical approach for the stronger concept of exact controllability (total controllability) is provided. The proposed control problem is a nonlinear fractional differential equation of order α∈(1,2]\alpha \in (1,2] with non-instantaneous impulses in finite-dimensional spaces. Furthermore, the numerical controllability of an integro-differential equation is briefly discussed. The tool for studying includes the Laplace transform, the Mittag-Leffler matrix function and the iterative scheme. Finally, a few numerical illustrations are provided through MATLAB graphs.

Keywords

• fractional differential equation
• non-instantaneous impulses
• total controllability
• mittag-leffler matrix function
• 34a08
• 34k45
• 93b05
• 34g20