Analytical approach and stability results for Caputo generalized proportional fractional differential equation involving two different fractional orders

Abstract

The results presented in this research paper investigate the existence, uniqueness and stability for a new class of Caputo generalized proportional fractional differential equation involving two different fractional orders. We expose and highlight some of the characteristics of the generalized proportional fractional derivative. We established the existence and uniqueness results by employing Schaefer fixed point theorem and Banach contraction principle, and also we investigate different kinds of stability such as Ulam-Hyers and generalized Ulam-Hyers stability. As application, we provide an example to demonstrate our theoretical results.