A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects

Authors

  • C. S. Varun Bose Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India
  • R. Udhayakumar Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India https://orcid.org/0000-0002-7020-3466
  • V. Muthukumaran Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamilnadu, India
  • S. Al-Omari Department of Mathematics, Faculty of Science, Al-Balqa Applied University, Amman, Jordan

DOI:

https://doi.org/10.37256/cm.5120243539

Keywords:

Ψ-Caputo fractional derivative, controllability, fixed point theorem, infinitesimal generator, impulsive effects

Abstract

In this article, we studied the approximate controllability of Ψ-Caputo fractional differential systems. We prove the sufficient conditions for an abstract Cauchy problem invloving infinite delay, impulsive and nonlocal conditions. The result is shown by means of the infinitesimal operator, semigroup theory, fractional calculus, and Schauder’s fixed point theorem. First, we prove the existence of the mild solution and demonstrate that the Ψ-Caputo fractional system is approximately controllable. Finally, an example is given to analyse the obtained results.

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Published

2024-01-05

How to Cite

1.
Varun Bose CS, Udhayakumar R, Muthukumaran V, Al-Omari S. A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects. Contemp. Math. [Internet]. 2024 Jan. 5 [cited 2024 Feb. 27];5(1):175-98. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3539