Controllability and qualitative property results  for Ambartsumian equation via  chi- Hilfer generalized proportional fractional derivative on time scales

S. Manikandan; Seenith Sivasundaram; D. Vivek; K. Kanagarajan

S. Manikandan Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.
Seenith Sivasundaram College of Natural Science, Engineering and Mathematics, Daytona Beach, FL 32114, USA.
D. Vivek PSG College of Arts \& Science, Coimbatore-641014, India.
K. Kanagarajan Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.

Abstract

In this study, we discuss the existence, uniqueness, and controllability results for an Ambartsumian equation with impulses using the $\Xi$-Hilfer generalized proportional fractional derivative (PFD). Common fixed point theorems are employed in our analysis. We achieve a few suitable conditions for existence, uniqueness, and controllability.