Abstract
AbstractIn 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\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.
Highlights
Sometimes, integer-order differential equation becomes inadequate to model some physical phenomena such as in anomalous diffusion
The main advantage of studying fractional order systems is that they allow greater degrees of freedom in the model
The Mittag-Leffler function is a generalization of the exponential function, and it plays an important role in the solution of the fractional differential equations
Summary
Integer-order differential equation becomes inadequate to model some physical phenomena such as in anomalous diffusion. The first kind of changes takes place over a relatively short time compared to the overall duration of the entire process Mathematical models in these cases are developed using impulsive differential equations. Many researchers have shown their interest in existence, uniqueness of solutions, stability and controllability of impulsive problems with non-instantaneous impulses [12,13,14,15,16]. Muslim et al [12] investigated existence, uniqueness of solutions and stability of second-order differential equations with non-instantaneous impulses. Wang et al [19] discussed controllability of fractional non-instantaneous impulsive differential inclusions. None of the research papers have so far discussed the numerical approach for the controllability of the non-instantaneous impulsive differential equation of order α ∈
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
