Existence and stability for Ambartsumian equation with -Hilfer generalized proportional fractional derivative

Elsayed, Prof. Dr. Elsayed M.; Manikandan, S.; Kanagarajan, K.; Vivek, D.

Existence and stability for Ambartsumian equation with -Hilfer generalized proportional fractional derivative

Document Type : Original Article

Authors

¹ Department of Mathematics, Faculty of Science, King Abudlaziz University, Jeddah 21589, Saudi Arabia.

² Department of Mathematics, Faculty of Science, Mansoura 35516, Egypt.

³ Department of Mathematics, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641020, India.

⁴ Department of Mathematics, PSG College of Arts \& Science, Coimbatore-641014, India.

Abstract

The main objective of this paper is to study the Ambartsumian equation in the sense of Hilfer Generalized proportional fractional derivative(HGPFD). The existence and stability properties of solution are studied. The technique used for study is fixed point theorem and Gronwall inequality. Ulam-Hyers-Rassias stability of the solution is also investigated.

Keywords