Qualitative analysis of solution to integral multi-point boundary value problem of Ambartsumian equation with tempered $\Xi$-Hilfer fractional derivative

Abstract

This paper deals with the fractional order Ambartsumian equation with integral multi-point boundary conditions. The reported results discuss the existence, uniqueness and stability for the solution of our proposed equation. We prove the main results by the aid of fixed point theorems and Ulam's approach. An example is included to illustrate the results.