Existence and stability for a boundary value problem of Ambartsumian equation with -Hilfer generalized proportional fractional derivative

S. Manikandan; D.  Vivek; K.  Kanagarajan; Elsayed M. Elsayed

doi:10.5269/bspm.64848

S. Manikandan
D. Vivek
K. Kanagarajan
Elsayed M. Elsayed King Abdulaziz University, Faculty of Science, Mathematics Department, P. O. Box 80203, Jeddah 21589, Saudi Arabia.

Abstract

In this paper, we prove the existence and uniqueness of solution for the mixed boundary value problem of Ambartsumian equation using -Hilfer generalized proportional fractional derivative(PFD). The main principles applied to investigate our results are based on the standard fixed point theorems. We dewell in detail on some results concerning the Hyers-Ulam type stability. We verify our result with an illustrative example.

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