Analysis of Non-Local Integro-Differential Equations with Hadamard Fractional Derivatives: Existence, Uniqueness, and Stability in the Context of RLC Models

Abstract

In this study, we focus on the stability analysis of the RLC model by employing differential equations with Hadamard fractional derivatives. We prove the existence and uniqueness of solutions using Banach’s contraction principle and Schaefer’s fixed point theorem. To facilitate our key conclusions, we convert the problem into an equivalent integro-differential equation. Additionally, we explore several versions of Ulam’s stability findings. Two numerical examples are provided to illustrate the applications of our main results. We also observe that modifications to the Hadamard fractional derivative lead to asymmetric outcomes. The study concludes with an applied example demonstrating the existence results derived from Schaefer’s fixed point theorem. These findings represent novel contributions to the literature on this topic, significantly advancing our understanding.

Keywords

• boundary conditions
• fractional differential equation
• Hadamard derivative
• fractional-order RLC circuit