Differential equations with variable order generalized proportional Caputo fractional with respect to another function: existence and stability

This study is concerned with the existence and stability of solutions of a class of initial value problem for fractional differential equations with a variable order generalized proportional Caputo fractional derivative with respect to another function. The statement of the problem is discussed and compared with the existing in the literature. Existence results are studied and the Hyers-Ulam stability is defined and established. The approach is more broad-based and the same methodology can be used for a number of additional issues. Copyright (C) 2024 The Authors. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/)